Of course.
It'll be a rocky start for sure. I started at the beginning of season 6. Went from Bronze 5 up to Silver 4 by the end of the year. I then hit Platinum 5 at the end of season 7 (it's a lot easier to climb once you know what every champion and item does, and what champions combo well together such as
or
) . Depends on how much you play, how consistent you are, and how much you enjoy the game. Yes, how much you enjoy the game will make an impact, if you get tilted/angry/frustrated easily then learning will be rough since you spend more time being angry than realizing what you did wrong.
Don't be intimidated by players who've be playing for a long time, it doesn't mean they are good at the game or that they have learned anything meaningful in that time. I'm Plat, and that doesn't mean I'm a pro or anything, but I'm better than a silver player whose been playing since season 1, and it has nothing to do with play time, it about learning the game. I'm actually ass mechanically, but I know where and when to be somewhere, and that's the best way to learn in my opinion.
As to how do you know if you're playing well? If you feel like you're getting carried in every game but have like a 60% winrate after 200 games. You aren't getting carried every game, if you were to AFK at level 1, your winrate would be like 30% or less so you are a main contributor in winning your games. As a new player though, I'd be less concerned of if you're getting carried, and more concerned about what the fuck the enemy champions do and what your teams champions do. Essentially, just embrace that you're garbage at the game and just be concerned on learning, we all had to get to a point where we can instantly understand a situation.