Certainly, the filling of the Holy Spirit is primarily a New Testament doctrine. However, I could not confidently say that John the Baptist was the first man filled. Consider what is said about Bezaleel in Exodus 31:2-3 - "See, I have called by name Bezaleel the son of Uri, the son of Hur, of the tribe of Judah: And I have filled him with the spirit of God, in wisdom, and in understanding, and in knowledge, and in all manner of workmanship."
Perhaps it is referring to something impersonal. This is also a
possibility in the reference to Joshua in Deuteronomy 34:9 - "And Joshua the son of Nun was full of the spirit of wisdom; for Moses had laid his hands upon him: and the children of Israel hearkened unto him, and did as the LORD commanded Moses." Joshua was full of the spirit of wisdom. This may not have been a personal filling of God's Holy Ghost, but surely the "spirit of God" and the "spirit of wisdom" come from the Holy Ghost.
In one more illustration, Micah testified in Micah 3:8 - "But truly I am full of power by the spirit of the LORD, and of judgment, and of might, to declare unto Jacob his transgression, and to Israel his sin." Again, the wording is not as strong as in the New Testament, but there is something here. If it is not the filling of the Holy Ghost, it is very close.
In conclusion, there was some form of the filling of the Spirit in the Old Testament. However, as with the indwelling of the Spirit, it was not available to every believer but was given to those with a special work from God. Bezaleel made the furniture of the tabernacle; Joshua led Israel into the Promised Land; Micah prophesied in a wicked age. God filled them with His Spirit in order to enable them for the task that was given to them.