I pulled my copy of the serialization book off the shelf and attempted to find the first hammerless entry. I think I found it as ser#55296; a DH 30 inch Damascus 12g. But, I know that book isn't always correct?
Also, looks like it lists 24822 as the first top lever; a grade 2 10 ga with 28 inch .
I'm on a roll, it lists the first gun in the book, ser# 1444 as a 16 gauge, but I find that hard to believe; it lists a grade 3 with laminated 28 inch barrels ser# 12990 as the next 16ga. But, the Parker Story has a table that lists an underlever B grade, ser# 15566 as the first 16ga. A mystery here....
The first 20 ga I could find was an underlifter, ser# 4634 in undetermined grade but with Damascus barrels.
The first 10ga listed is an underlever ser# 2088; a low grade with decarbonized steel barrels.
Of course, I did this with my old eyes, so don't take any of this to the bank. I found it to be an interesting exercise.
I wonder if Chuck can shed more light on Parker firsts...... preferably as a Parker Pages article.

Chuck?