You could add onChanged_actions to the two fields, then when either is modified you can check to see if both are populated. If so, then you can do the various checks which you need. Ensure that both have ‘not empty’ validation so that the form can’t be submitted without them both having been populated / changed.
I’d suggest using moment.js (https://momentjs.com/) which is available ‘by default’ in BF for dealing with dates, it provides all sorts of manipulations and comparisons. Then I’d be inclined to use a toastr message to say ‘Hey you can’t finish before you start’, or 'Are you sure you got your date of birth right ‘cause it doesn’t look like you’re old enough for this’.