Best I can come up with would be to have
Unfortunately, this would mean that the place I edit the date would be different than the place I view the date
First thing that comes to my mind is to use automation to write today’s date when you create record.
There might be some more elegant solutions 
How would I do this?
I saw something about a limit on automations. If I had one automation per record, I imagine that I would bump up against that rather quickly(?)
Well that depends on the amount of records you will be making and plan you are on. You can see limit of each plan on https://airtable.com/pricing
If you dont need to have date editable you can just use formula.
As for automation, you would need a formula field in the base with Today() function.
Than use trigger “when record is created”, and insert field with Today() formula into the date field you need to be editable after.
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