You can get a Burner number for Tinder (or whichever dating app you're using). And, if things go well, you can keep the Burner number as a great way to interact with semi-strangers and others in your personal and professional life who don't need access to your real phone number.
It is not possible to open a Tinder account without a phone number because it is mandatory for all users of Tinder. However, there are fake phone numbers for Tinder that can easily be used to only get the verification code for Tinder to open the account.