C Replacements for srand() and rand()

I'm trying to make a game in C fit under a 3KB limit, and to do so I want to remove all standard library references. The only header I want to have in my program is windows.h and so far I'm doing pretty good.

The only external references I have are one call each of rand(), srand(), time(), and getch(). This may seem like a lot for a game under 3KB, but the time, rand, and srand functions are only so that when the game starts it can have a random seed.

rand to get the numbers, srand to set the seed, and time to get random seeds. So if I could find a way to get rid of the excessive random generation procedure, I could get rid of 3/4 std library functions. I'm not so sure what to do about getch though, but ill focus on that later.

Some people have reccomended xorshifts, but it seems like that requires the type uint32_t, which belongs to stdint.h. I also tried using integers instead, and while the resulting number was random, it was random in the sense that the number given back was random, yet you could depend on it giving you that random number each time. I could give it time as a sort of seed, but then id still have to use the time function. Is there something I'm overlooking, or should I use a different method?