Usually I don't fuss over small details like birthdays, favorite foods, and things of that nature. What sucks me into their characters is really their personality and how they would react to different scenarios, and each other.
And said scenarios don't even have to do anything with a possible story. It's more of an exercise to flesh out your characters' personalities. Like how would each one react if they got stuck in an elevator?
Another important thing to ask oneself is what their goals and motivations in life are. I like to focus on this particularly when I'm formulating a story for them, since it's essential for character development arcs.
Tying in with the above, for forming plots, sometimes things don't come all that naturally, you have to inject some element to get a story rolling, to get the characters motivated and driven toward something.
For example (mild spoilers ahead for my webnovel Secunda), I had a character, an older man. He had to get involved into my heroine's plot line somehow. Now for context, she has a monster skull that has a symbiotic relationship with her. I wanted the older man to put that in jeopardy, but I had to come up with a reason for him to want the skull. I raised the stakes by giving him a disease that he thinks the skull can cure. So by 'artificially' injecting an element into his backstory that wasn't there before, I gave him a reason to exist in the plot and provided a basis for his own story arc.