Yes, this is possible in a couple different ways.
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Passwordless Connections enable you to sign up & login users with phone identifiers and an SMS delivered OTP code. Documentation: link and and link.
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This year we have made additional improvements to require users that sign up with a phone number (or email) on a database connection to also verify their number during sign up. Phone number and email verification on sign up are both available today. Email Verification Announcement