Yes! That's what Crossmint is for!
You can buy NFTs without having crypto or a wallet like Metamask or Phantom!
By the time you are done buying, Crossmint has already created automatically a Crossmint NFT wallet for you and the moment the payment is done, automatically, the NFT will be stored on that wallet.
You can always access it by logging into your Crossmint account.
Watch the experience of buying an NFT with Crossmint and accessing your Crossmint wallet: