It depends. What are you willing to risk to get what you may want?

You have only been there a year and you are eager and motivated. This is great to hear. It also sounds like you enjoy writing software, also great.

Here is what you do not want to do: become a PITA.

Stop talking to management so much (at least for now), they probably are getting tired of it.

Also try to fit into the culture where you work (at least for now).

And absolutely always ALWAYS be a team player. Even if the senior doesn't know as much about the product as you do right now. Offer your help and be nice about it. Don't take things personally, even if someone is being rude to you. Also try to look for people who you admire professionally and help them whenever you can.

In the mean time focus on your skills and keep improving your corner of the world.

What will happen, sooner than later, is that those people you helped will remember you. And when they are in a position to affect positive change, they may return the favor.

While you are doing this, make mental notes of where you want to be and definitely do shop around. By being aware of the real world situations, you'll be better equipped to recognize a better situation.

Best of luck to you!