First of all, despite the absence of a cachet, you do indeed have a First Day Cover for this stamp.
Secondly, the short answer to your question is, "No."
As I recall, not certain, but the addition of the words "First Day of Issue" did not come along until the early 1920s. Someone into the later stuff can tell you exactly when, but I think that some of the earliest of that type were serviced by George Linn or A.C. Roessler. Where the first day of issue for a stamp is known, covers cancelled on that date are recognized in the hobby as FDCs.
Where the first date of issue is not known, or no such cover exists, the hobby defers to the Earliest Documented Use. Such covers must be certified for that, however. Here is an example of the latter, in which the first day has never been determined, so the EDU is as close as anyone can get.

This last is a new discovery which Scott does not yet list.