Same thing happened to me, I could go into the first level but since the controls only allowed me to turn the knob up and down for whatever reason, I reset my browser. The image here is what's shown in the level menu when opened again in the game (I'm on chrome).
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Huh, that is super bizarre. What this indicates is that you somehow set your score on level 1 to a negative number, making the game think it isn't unlocked. I'd try to either reset your browser cookies somehow or to open the game in an incognito tab / another profile or something. Apologies! Will definitely include a "reset save data" button in my next jam submission.
Unfortunately, as long as you're hitting return to properly move through the menu, I can't tell you why you were unable to move. Hopefully if you open another window it won't be the case.