I love the concept and the cartoon art style is charming. (I do find that the music doesn't really fit the mood.) Looks like we both made a game about counting down block push moves :) Thanks for finding my game earlier.
I got about half way through (counter = 5) and I feel like the difficulty is a bit hard, at least for me. I guess continuing our discussion from my game ("I'm usually not the biggest fan of explicitly tutorializing basic puzzle mechanics"), I would disagree and I think that's what this game needs is a bit more basic introductory levels.
As an example, you have a mechanic (or "trick") of being able to push a >2-bomb into a 1-bomb, causing the 1-bomb to explode and the cat to survive. This technique is used in many puzzles, but it is first introduced on level "10" (the fourth level) in a fairly complex puzzle that's hard to execute even if you know the trick, which you don't yet. So having a bare minimum level to introduce new mechanics would help with the difficulty spikes.
Very charming game all in all!