I've flown IB MAD to JFK many times, I have Global Entry.
My fastest time through - wheels down to standing at the exit - 30 minutes. Longest, about one hour.
Getting on a flight leaving LGA at 3:45 - I would say you have no chance of doing that and I am sorry. The lengthy and unpredictable (as well as predictable) delays would start as soon as you left JFK.
I would give myself 4 hours between flights at very minimum. With no checked bags.