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Plastic DogGo to pages 30-31 of Lipset's encyclopedia for E cards. Anyway, according to Lipset Vic Aldridge played in 1917-18, but didn't play again until 1922 (but has a card in the set). Gabby Harnett played sparingly as a rookie in 1922, and has a card as well. This dates at least some of the set to 1922; doesn't mean that some of it couldn't have been issued in 1921 as well, but if you absolutely positively have to have a card issued in the first year, I would go with one of the other sets listed above.
But what is a rookie anyway for a vintage player? First national card? First card? First paper product? First picture? First individual paper product? First paper product small enough to be graded by SGC or PSA? First card of a recognized set? First card of a recognized set that more than one person can acquire? First card distributed as part of an incentive to buy a product but not as the product itself? First card better than a crude drawing? What about generic pictures? Do pins count? Do premiums count if the same company had a regularly-issued card? What about premiums without regularly issued cards? What about strips, exhibits, premiums too large to be graded? What about foreign cards? Do Canadian cards count as foreign?
Suffice as to say that noone has a complete rookie card collection, as the 1894 Alpha Photo and Engraving cards are the rookies of McGraw, Jennings, Joe Kelley, etc. and they all reside in Baltimore.