Need desperate and urgent help with sleep training

So I don’t know if it is me or if it is my little one that got us here. But here’s the story

From day 3 (basically since we got home) he wouldn’t sleep properly in his crib. Or the bed or anywhere but my lap. Initially I was thinking he was waking up frequently because he was constantly hungry. But he eats a decent amount every day. He is currently 4.5 months old (exactly 20 weeks) and the early months he would sleep in his crib for a little bit - maybe 5 minutes- then would wake up I would try to rock him out him back to bed another 5 minutes and then I would have to rock him for longer so he would sleep again. Sometimes he would actually not even go back to sleep after that 5 minute nap and would be cranky fussy and I would be miserable. Slowly it turned into me never putting him to his crib to sleep because I needed the baby to stay calm so I could stay calm. Otherwise I was exhausted both physically and mentally. This way I was only exhausted physically but at least I was mentally happy. Well it’s 4.5 months and both my husband and I can’t handle the physical exhaustion. But the baby still doesn’t like to nap in his crib. Here’s a typical day

Wakes up sometime between 7:30 and 8:30.

Stays awake for 1.5-2 hrs.

Gets cranky/sleepy so I try to feed him and put him to sleep.

Naps on my lap for 45-90 mins

Wakes up.

This goes on for 3 naps a day.

Then sometime between 7:30 and 8:30 we start bedtime routine. Pajamas, story, bottle then sleep.

We put him in his crib

After that starts the struggle. Some days he sleeps for 4 hours some days 1. Wakes up.

We try to rock him back to sleep with no success.

We feed him then put him back.

Usually until 2 or 3 AM we manage to get 1 stretch of 3 hours at least.

After 3 AM he wants to sleep on my lap again otherwise he won’t sleep for longer than 1 hr.

Today he woke up basically at 6:15AM and for the last 2 hours we’ve been rocking him putting him to his crib with no luck.

He sleeps a total of max 12-13 hours a day. Since he was a week old he never slept for more than that.

Is it me? Is it him? What can I do? Please help with suggestions as to what worked for you especially if you have a problem sleeper like my little one.

I am overwhelmed by the internet so I would like tested and true solutions.

One weakness I have is the baby crying. I can’t handle it and everywhere I read it says don’t let the baby cry, you can’t spoil a baby etc etc...