This is too easy to not screw it up. All you need to have is a calendar for everyone's birthday. Make sure there is a bit of time and money in place.
This works while your team is still small (less than 30), but after that you will want to build this out as a policy among your direct reports.
Setup a calendar
This is easy to do, just add another calendar entitled "Employee Birthdays" and keep it updated. This is easy if you have proper on-boarding and off-boarding processes.
Let employees know this calendar exists. This should be an opt-in rather than opt-out kind of thing. Of course, they can opt-out at any time. Check local laws and customs. This may be too touchy in some places (GDPR, etc), but this part is left as an exercise to the reader.
Keep it cheap and cheerful
If possible I think it is nice to personally, and privately, offer a congratulations along with a small token of appreciation. Maybe a festive bottle of wine or champagne or something like that. Not more than $20.
Or, just have the company buy them lunch for the day.
Make it appropriate
Cake or alcohol may not always be the best gift. Give it some thought and see what you can do to make it more personal.