The secret to the 60's (and 700's) sound: real drums, real amps moving air in a nice'sounding room, captured by microphones that today cost as much as a used car.
Minimal overdubs, no pitch correction, no quantization, no copy-and-paste arrangements, no canned loops, no comping.
I've tried to replicate it, but it never fails - I can't resist the urge to "fix" everything.

But it's certainly doable with todays technology...absolutely.   Just don't give in to those urges Bit.  Stay strong.