I’m having trouble coming up with a formula that chooses the earliest of up to 12 dates with times. I’ve seen other questions that are similar but this involves times too. The Time 1 … Time 12 variables are from a lookup in another table. They might be blank.
Are they lookups in the same field? If so, you can use a rollup field.
However, because you have several different fields , I’m guessing a rollup won’t work for you.
Here is a different formula designed for four different date/time fields. You can extend the pattern to add more date/time fields. Note that it might not work for lookup fields, because lookup fields are quirky. You might also need to set the timezone formatting options on the formula field.