First Strike Coins

The U.S. Mint has no First Strike program for the minting and distribution of its coins. However, the Mint sometimes does "first strikings" of new coins, but the "first strikings" are ceremonial and usually are for only two coins, which are not set aside but are put into the regular inventory of the new coins. It is probably from these ceremonial strikings that promoters came up the idea of First Strike coins.
PCGS and NGC First Strike Coins
The premier coin grading services that grade First Strike coins are Professional Coin Grading Service (PCGS) and NGC (Numismatic Guaranty Corporation). These two firms' positions on First Strike coins more clearly explain what First Strike coins really are.
The PCGS website does not discuss First Strike coins, but does post the U.S. Mint's position on First Strike coins. However, the NGC website designates as First Strikes coins that were shipped from the U.S. Mint within the first month of their official release. PCGS says that for coins to be labeled First Strike, they must be received within thirty days of commencement of shipping (or have documentation that "proves" that the coins were shipped during the first thirty days of a coin's production.)
NGC does not assert that the coins eligible to be labeled First Strike are among the first coins struck but are coins shipped within in the first month of release. Further, NGC includes in the First Strike category "coins of early or first release. A general term for these coins is first strikes."
In reality, the NGC position on First Strike coins offers the best definition: coins of early or first release. While First Strike coins may be from the first strikings of a new set of dies, in reality there is no way for graders or promoters of First Strike coins know that the coins they are promoting were from the first strikes of new dies.
First Strike Not Trademarked
Some websites maintain that PCGS trademarked First Strike; however, a search of the U.S. Patent Office's website does not evidence that, and a search of the PGCS website did not find any claim of having trademarked First Strike. NGC asserts there is no trademark for First Strike and that it is a generic term in the coin industry.