Reading Angela Duckworth at a young age helped. Whether it's true or not, the placebo effect on grit is amazing. Have a fragile ego that makes the possibility of failure hurt more than the pain of frustration. When you feel like giving up, realize that's like any other emotion and you can choose to act on it or not separate from it existing.
I wouldn't describe wanting to give up as primarily an emotion to me, but rather a function of available energy, or something akin to pain. I guess pain is maybe technically an emotion, it's certainly not something trivially dismissed on a whim. Anytime I've burned out on something, I just have no energy left and am physically pained by having to keep at it.
Put yourself in situations that test your grit. Then learn to adapt to the situation at hand. Rinse and repeat until the mental switch flips in your mind where you realize all dire situations are not really dire, and workable so long as you navigate them with a clear head.
For example, in my youth I was very fearful of becoming destitute. So to assuage that fear I became temporarily destitute: no money, no connections, and nothing to fall back on. Cue awful physical conditions like (attempting) to sleep out in hyperthermic temperatures with endless wind chill (something I've done before as a child), lack of food and water, and lack of resources. It's not bad for a month, but after that the realization will hit you that you are truly and utterly fucked if something goes wrong. Grossly miscalculate your travel from city to city? You now ran out of water, and will have to find some shelter when the night rolls in. All alone in the wilderness, will you make it in time to place with fresh water, or will you die before that happens? Uncertain. But all you can do is keep moving forward and play the hand your dealt. After a while the feelings you encounter aren't so potent, and you learn that all you can do is keep persevering in spite of everything.
A similar example is school sports. If you're an athlete you know what it's like to push yourself through the pain, drudgery, and exhaustion (something that no doubt had helped me in the above). You have a race to finish, so you might as well keep going and give it your all. Same with training: wake up at 4am, travel, practice for 3 hours with little sleep, and repeat for the season.
The trick is to be put into situations that test you and then it's up to you to pass. Once you pass, that grit you built will stay with you forever. It's mental, more than physical (but physical ailments and ill-health will greatly decrease your capacity for grit).
Unfortunately, it takes getting away from the modern coil and routine -- something that's not easily available to adults with responsibilities, careers, bills, and so on. So it's greatly unlikely you'll build grit, unless -- unsurprisingly -- you force yourself into the perilous situation of throwing it all away.