CRY IT OUT???

How old does a baby need to be before you let them "cry it out" when they fight sleep??? My 3 month old wants to fight sleep even when he's been up for hours with momma and daddy playing. He'll get fussy and rub his eyes so I know he's tired. but when I lay him down for a nap he screams and cry's till you go tend to him. I have to literary have to stand there holding the pacifier in his mouth cause he'll cry when he spits it out. He sucks on that thing like it's going out of style. I always check everything first to see if it's that why he's crying. I check his diaper, see if he's hungry, see if he needs a burlp. I don't want to let him cry cause IDK if he's old enough to let him "cry it out" when he's throwing a fit and I don't know what to do. When I let him sleep on me he's fine and sleeps good..... it's only when I put him down in his crsib he gets fussy and won't go to sleep half the time. Except for night time, he sleeps great at night. All the way through from 9:00pm-4:30 or 5:00am. See I don't get that, why does he do that?? But back to my question, how old must a baby be before you left them "cry it out" when they're fighting sleep or throwing a fit???

EDIT:

I been trying laying him down when my brothers are eating cause they watch TV while they eat and its quite. George sleeps for maybe a full 3-4 hours and when he wakes up and eats (he eats 24 oz a day) he's happy. I'm so glad I contacted other moms on here especially since he's our first. My mom is so busy I don't know how she does it. Also I changed his bedtime to 6:00. He still wakes up around 11-11:30 to eat but then goes right back to bed and sleeps through the night till 5 or 6 in the morning. Thank you all for your help and advice. 😊