currently it's not supported using built in business logic, you can see similar idea at  closed on date of a defect cannot be a future date
I suggest to vote for it and add comment about prevent past dates.

What you can do today, which is not easy but doable:

1. create business rule that alerts if someone adds date that is before date X (some date).
2. create automation that will run daily and will use rest api to update this business rule definition changing the date to "today"

This way you will have updated business rule that prevents users from entering past dates.

currently it's not supported using built in business logic, you can see similar idea at  closed on date of a defect cannot be a future date
I suggest to vote for it and add comment about prevent past dates.

What you can do today, which is not easy but doable:

1. create business rule that alerts if someone adds date that is before date X (some date).
2. create automation that will run daily and will use rest api to update this business rule definition changing the date to "today"

This way you will have updated business rule that prevents users from entering past dates.