How do I tell the professor that I am burnt out and I want to move on
You are in a bad spot and it is difficult to diagnose the disease, much less the cure. It may be that your advisor is inexperienced - some things you say indicate that. But as commenters have implied, some problems worth solving are just hard - damn hard. I once worked on such a problem and had to abandon it, but the professor agreed and we found a better one. 

However, it may be that your "best" solution is to find a different advisor. That can be difficult (or impossible) as there is department politics to consider. Some large departments even have factions. The radical solution is to change universities and thus find a different professor with different ideas. 

But a student working on an extremely hard problem is itself a problem since it takes time and the student would like to actually graduate before the Sun goes nova. I also worked on problems that were too easy (mathematics) and hence had no real merit. The trick is to find the sweet spot of a sufficiently hard but do-able problem. Not all professors have the ability to to that regularly. 

But you need to judge. If the problem is hard, but its solution would be a significant advance and you have the time and resources to pursue it, it can result in a big win. But the win isn't guaranteed. 

However. It also sounds like your current advisor is truly invested in you. Two meetings a week shows commitment. You won't always find that in an advisor. 

You might try two things. First is to have a conversation about the likelihood of actual success in a reasonable time frame. The other part of the conversation is to try to set a limit on attempts and explore alternative problems that don't completely ignore what you have done so far. If your advisor is, in fact, invested in you and not just in the problem itself, that conversation might be possible. 

As a first year doctoral student it isn't yet time to panic, in fact. Significant things take time and focus.