There are several aspects to this. One is APM (actions per minute) and how you as a human are interacting with your computer using the mouse and keyboard and monitor.
What @Scout_More_Often wrote is a good way to grow your economy at minimal cost of APM and attention. You can also solve one of the problems @FtXCommando mentions by un-pausing mexes while they are being upgraded (if you remember to do it). Whatever mex is being upgraded by the engies, unpause that one, and it's like you have 2 extra engineers assisting the upgrade.
I think there might be a mod that automatically un-pauses upgrading mexes when engineers start upgrading them but I don't know it offhand.
Separately, one of the things that slows down mex upgrades is stalling on mass or energy. If you spend too much on other things (like making naval factories and frigates) it will be difficult to afford the mexes. Finding the right balance between growing your economy and making weapons is very important. Depending on what your opponent does, you might have to make a different decision about how to allocate your resources.
You also need to balance between making mexes and making pgens. If you overspend on making power generators, that will slow down your ability to get mexes upgraded. (And if you don't make enough power, the power stall can make your upgraded mexes pointless. Why upgrade a mex to get +4 mass/second if you're going to have a power stall that costs you 4 mass/second?) Farms often gets T2 on his ACU in order to make 1-2 T2 pgens, because that's cheaper than upgrading a factory to T2. And often he goes to T3 on his ACU for the T3 pgen, for the same reason.
You can also look for mass from other sources, which primarily means reclaim. Rocks, dead units from battles, or if you make a T3 pgen, you can reclaim the T2 pgens and T1 pgens.
I have to disagree with @FtXCommando , if you're playing Rock spot on Seton's, you're not going to make a conscious decision on every mex upgrade. In many other kinds of matches, it will be a conscious decision, at least for the first 10+ minutes of the game. At some point your economy might become big enough that you don't have to give each mex upgrade that amount of personal attention. For some maps (Seton's, Dual Gap, Astro), it's basically taken for granted that you will be upgrading a lot of your mexes.
It's also good to do things in the right order. Meaning (unless you can afford to do it without stalling) you only upgrade 1 mex at a time. Stalling while you try to upgrade two mexes is wasteful. That's also why you use engies to assist. Two mexes that are both halfway upgraded gives you 4 mass/second. One t2 mex + one t1 mex gives 8 mass/second. And you generally want to get your safe mexes up to t2 before you start putting mass storages around them.
If you want to get good at growing your economy, I would suggest watching replays of people like Farms from their POV (during a replay, you click on their name in the scoreboard to view from their POV). Watch what decisions they make and how they keep their economy balanced. Do they stop making engineers at some point to avoid wasting mass on that? How important is reclaim to avoiding an energy stall early? What choices do they make that seem strange to you? If they're doing something, they probably have a good reason for it, so you should try to figure that out.
Then when you hit a wall, ask @CheeseBerry to train you.