It looks like it's been over four years since this was addressed here. Old answers to this settled on a single input for the entire date (with a hint for formatting).
But I see that Google uses a drop-down for the month in their sign-up form:
And the US goverment web design standards site uses three input fields: https://playbook.cio.gov/designstandards/form-controls/#date-input
Additionally, what do you think about the label? Birthday vs. Date of Birth vs. Birth Date