Thanks for leaving a message on the existential crisis hotline. Your question is a really tough one to answer because there's a lot of stuff that breaks down at really small scales, including time. I can't tell you what time is, but I can tell you some stuff we know about it, and point you in some directions to learn more.
If you're super interested in this stuff, I highly suggest considering a career in theoretical physics, since that's where the people exploring the very edge of what we know about time hang out. It's not as hard as it sounds... there's definitely a lot of math, but a lot of what you learn is history. You'll learn how we know what we do about time (and other things), so you can build on whats already been discovered.
So, here are some really cool facts about time...
Increments of time have a finite scale (the planck length), so it actually progresses in discrete chunks, even though there's no way we could perceive that. Here's a very cool video discussing this in detail: https://www.youtube.com/watch?v=-6rWqJhDv7M&t=2540s
Scientists believe that time and space switch roles inside a black hole. In your day to day life, time only moves in one direction but you can move in every direction through space. In a black hole, matter can theoretically experience time in multiple directions but can only travel through space in one direction: towards the singularity. Here's a really cool video about jumping into black holes: https://youtu.be/_8bhtEgB8Mo
Sean Carrol has a podcast called Mindscape that I recommend highly if you want to fill your brain with physics and other fun science stuff.
Time and entropy seem to be tied together. At the moment of the big bang, the universe was highly ordered. It was literally all in one place and although we don't know what it was actually made of, it was hot as fuck. It went from that to being quarks, and from there became more and more disorganized, forming assorted atoms and molecules. Entropy is the statistical tendency of things in a closed system moving towards a ground state (or lowest energy state) over time, like cream spreading in a cooling cup of coffee. At first, it seems like living organisms kind of mess up that trend, but we're actually fun little entropy machines, and we're not in a closed system. We get a ton of energy from the sun. Event oil and gas energy originally came from plants that took the energy from the sun. When the sun burns out, we'll be mushy cold cups of coffee again. Time as we understand it is a way to measure this inevitable change.
CERN and other particle accelerators all about studying this stuff... they knock particles together to recreate the conditions of the early universe, at the moment when time literally came into existence. You might want to look into attending a public lecture. Astrophysicists often discuss time as well, so if there's an observatory near you, you can reach out. It can be tough finding mentors for this stuff among your peer group, but scientists absolutely love sharing what they know. You just have to look for them where they hang out. :)
Lastly, the World Science Festival in New York is an amazing place to meet other people who ask the same questions as you.
