What Adam posted was along my initial thinking as well, it would work.
There may be other solutions to this that are more user/UI friendly.
One thing I was just thinking of would be if you had hidden fields next to each field you want to show as completed. Similar to what Adam posted but have them only show up when a checkbox after each section is clicked, or at the end of the form even. You could do this per field, which would get a little out of hand very quickly, or per section. MY example here is going to be very simple but hopefully it helps to illustrate my point. IT has a form rule that is essentially "when Section 1 - Date is no blank and Section 1 - Finished Checkbox is checked, show Section 1 - Validated". You could have other conditions in there as well.
And obviously nothing is shown as valid if there is no date. However it does not prevent submission in that case, you could add it in.
Hopefully that helps to show another option.