Maybe extend your brain with paper? When starting any activity where you'll need to think about strategy, get a piece of paper with STRATEGY written across the top and think on it as you go.

Playing Race for the Galaxy (RftG) might help. It's my favorite board/card game, but I'm suggesting it because I really think it's applicable here. There are several things about RftG that should help you develop macro strategy skills, and hopefully translate those to other games and eventually real life.

First, like many other European-style board games, RftG doesn't feature direct conflict (with the exception of takeovers; I don't usually play with those optional rules). This means that in a multiplayer game of 2 to 6 players, you can't directly attack another player, and they can't directly attack you. Indeed, you can (and should, as a newbie) ignore what everyone else is doing, and focus on building up your own galactic civilization. RftG isn't multiplayer solitaire, though - there are second-order ways to interact with other players, typically drafting on their actions to give yourself a boost, avoiding giving others drafting opportunities by choosing actions that will maximally benefit you and are least likely to prove valuable for other players, and taking actions at times that will be inconvenient for other players (this usually means Consume, the only mandatory phase). Newbies have difficulty noticing or taking advantage of multiplayer interactions, but they're what keeps the game fascinating as an expert. In my mind, the fact that you can ignore other people as a newbie is what makes RftG near-ideal for developing macro strategies.

Second, RftG throws a lot of randomness at you - random start worlds (which determine the bonuses you'll have at the beginning of the game), random starting hands, and drawing tons of random cards (many more than 1 per turn, typically). I also love Magic, but the real beauty of that game is in deck construction (either ahead of time in Constructed, or on the spot in Sealed). When actually playing Magic, you're drawing from a deck you've built, of only 40-60 cards, containing many duplicates (at the very least, basic lands). The randomness that RftG throws at you is much more like the randomness involved in opening up 6 packs of Magic cards and building a 40-card Sealed deck, except that you do it while playing the game instead of taking 20+ minutes in secret from your opponents. Of course, RftG would be pointless if this randomness were unfiltered. The distinguishing feature of RftG, as I see it, is the vast number of mechanisms it gives you for filtering randomness - you get to pick 1 of 2 random start worlds, 4 of 6 random starting cards in your hand, and through your choice of actions, you control when and what cards enter or leave your hand. This is because cards, in addition to being things that you can play (settling worlds and building civilization "developments" for victory points and gameplay bonuses), are also "money" that can be spent to play worlds/developments. (For example, to settle the Alien Toy Shop, you must discard 3 other cards - so choose the least useful cards in your hand.)

There are other nice things about RftG (remarkably, players take their turns simultaneously by choosing actions secretly and revealing them all at the same time - this is nearly unheard of outside of video games, and it makes the game go very fast), of course.

What all this means, when you're playing RftG, is that you're immediately faced with decisions - and if rationality means anything, it's making optimal decisions with the information that you have. From the first moment of the game, you have to look at the 8 cards in front of you and decide what kind of macro strategy seems most viable - do you go for straight up military conquest, which is aided by starting with military strength, and having easily conquered worlds in your start hand - ideally, worlds which will provide additional strength to your growing juggernaut. Or do you go for the civilian strategy of producing and consuming goods, which relies on having different bonuses and different cards? The strategies do blend into each other, and there are sub-types (e.g. there are economic empires that dominate rare element production, others that rely on genome production, etc. - which play quite differently). Playing with the additional mechanisms introduced by the expansions give you other things to look out for - the "first" and "most" goals reward players who are first to achieve some milestone, or who have the lead in some area (e.g. military strength).

Most importantly, because the randomness is continuous, you must monitor and potentially adapt your strategy as you go. In many games I've started with a civilian empire, only to notice that I had accumulated a bit of military strength and could go conquer some worlds, and ending up with more military worlds than civilian. Or vice versa. Sometimes I just muddle along and make micro-optimal decisions, but can't quite build the grand strategy I was aiming for - it does happen (although some of the time, if I were more skillful, I could avoid it, which is what keeps me playing).

As for actual macro strategy advice, I can tell you what I do, which may sound vague. When playing a new game, the first things I want to know are its end condition and its win condition (they can be different, and often are in European-style games; for example, one of the two ways that RftG ends is when someone has 12 worlds and/or developments in their civilization, but the winner is the one with the most victory points, which can easily be someone different than the person who triggered the end of the game). Then I want to learn the rules, focusing on things that affect the win condition (including things that negatively affect it, e.g. how I can be attacked). For example, in RfTG, all else being equal, having more cards in your hand is better. However, cards don't directly grant victory points (obscurely, they act as a tiebreaker in the case of equal victory points, which almost never happens). Cards are merely "potential" victory points, and must be either played or spent to play cards that will grant VPs. Therefore, the Explore action, which allows you to draw cards, doesn't directly contribute to winning. In fact, Explore is much more marginal than newbies often assume - (for the experts in the room, I'm going to ignore the other Explore for simplicity) it allows you to draw 3 and keep 2 cards, but everyone else gets to draw 2 cards and keep 1. Therefore, advanced players understand that Explore should be called only when you really critically need cards, in a much more dire way than anyone else does, and you have no other means of obtaining them. There are other means of obtaining cards (e.g. Consume) that are less likely to benefit other players so strongly.

Some "getting started" notes: RftG consists of the base game and 3 expansions at this time (#1: The Gathering Storm, #2: Rebel vs Imperium, #3: The Brink of War), which should be added cumulatively. The base game is 2-4 players, with the 1st expansion it's 2-5 players, and with the 2nd and 3rd expansions it's 2-6 players. I recommend the 2-player game for newbies, as it's easier to keep track of a single opponent. (There is also a "solitaire mode", but it plays differently from multiplayer.) Each expansion adds cards, which bring increasingly more complicated powers, but also make more strategies viable. As a newbie, I recommend starting with the base game and expansion 1, The Gathering Storm - that's a reasonable level of complexity, and contains important cards. When you get comfortable with the game, then add the 2nd and 3rd expansions.