Is 1.C3 a good move?

#1
Yes 1 c3 is a good move.
Black can play 1 e4 c6 and 1 d4 d5 2 c4 c6, so white can surely afford 1 c3.

As white you have one more move so you can play practically anything as the first move and it doesn't make your position somehow really bad. I don't think that 1.c3 is a good move but chess would be boring if people played only good moves. I play 1.b3 for example and I profit from the fact that people often don't know the lines there as well as in normal openings...
#6
AlphaZero ranks 1 c3 above 1 b3:
d4 > e4 > Nf3 > c4 > e3 > g3 > Nc3 > c3 > b3 > a3 >
h3 > d3 > f4 > b4 > Nh3 > h4 > Na3 > f3 > g4 > a4
Figure 31.
https://arxiv.org/pdf/2111.09259.pdf

It's playable, sure. But I wouldn't call it "good".
Logically, the purpose of 1.c3 would be to support 2.d4.
But white can already play d4 on move 1, without needing any immediate support, so 1.c3 is kind of ... unnecessary, at best.
If the white c-pawn had an opening choice, it would prefer to move to c4, much of the time. c3 is more of an "only in specific scenarios" move.

There are multiple ideas behind delaying an immediate d4. White may answer 1...c5 with 2.e4 and everything else with 2.d4, or he can even try to play 1.c3 independently - either as a reversed Gurginidze with 2.g3 3.Bg2 4.d4 or as a reversed Hanham Philidor or Black lion.
There is also the interesting Elshad system for white, which is 1.c3 2.Qa4 3.g4 against basically anything, which is just bad, but there was an entertaining book written about this system.
In regular chess, 1.c3 is about equal at best, but in 30 second and especially 15 second chess it is quite possibly the absolute best first move and is being used by many of the best ultrabullet and hyperbullet specialists.

No. 1. c3 is a terrible move as it does not help accomplish any of your goals in the opening:
Control the center: not good enough
Develop your pieces: only your queen, and takes away the c3 square for your knight
etc.

1. c3 is a bad opening because, Control the center with 1.c4/d4/e4. Control over the center:bad. Development: bad. And the c3 square is ment for the knight