I've USDT (Tether) on gate.io (which support SOL or other Solana tokens), but they don't support USDC.
In this case, what's the easiest way to convert/swap USDT to Solana's USDC?
Is it possible to send USDT to Solana's wallet (like Phantom), then swap it to USDC?
Yes you can send USDT right to Phantom wallet:
https://solscan.io/token/Es9vMFrzaCERmJfrF4H2FYD4KCoNkY11McCe8BenwNYB
Then you can use Phantoms built in swap, or use Jupiter Aggregator:
https://jup.ag/swap/USDT-USDC
However I wouldn't consider USDT to USDC explicitly a relevant question for Solana stack.
