No, White can not force a Caro-Kann. The Caro-Kann is specifically the position after 1.e4 c6 2.d4 d5.
caro kann
No, you can't even force a Reversed Caro-Kann as you can't force Black to play d5 and e5.
Just because you play the moves d4 and c3, that does not constitute a "White Caro-Kann". A lot depends on what else is played.
For example, if the e-pawn goes to e3, then it depends on what White does with his Bishop on c1. If it stays on c1, it's a Colle Koltanowski, if it goes to f4, it's a London System, and if it goes to g5, it's likely going to be a Torre Attack by transposition once White plays Nf3.
If the e-pawn goes to e4, then it depends on what Black has done. You could have some weird line of the Modern (like 1.e4 g6 2.d4 Bg7 3.c3, which could also come via 1.d4 g6 2.c3 Bg7 3.e4).
So again, the answer is NO, White can NOT force a Caro-Kann OR a Reversed Caro-Kann.
Can white use ,,,caro kann .....defence as his opening?