Here is a Transcription directly from the US Mint:

The United States Mint has received inquiries from consumers regarding use of the term first strike. The term has appeared in connection with the advertising and grading of 2005 and 2006 silver, gold, and platinum proof and bullion American Eagle Coins, and the new 2006 24-karat proof and bullion American Buffalo Gold Coins. Currently, there is no widely-accepted and standardized numismatic industry definition of first strike. Coin dealers and grading services may use this term in varying ways. Some base its use on dates appearing on United States Mint product packaging or packing slips, or on the dates of product releases or ceremonial coin strike events. Consumers should carefully review the following information along with each dealer’s or grading service’s definition of first strike when considering a purchase of coins with this designation.

The United States Mint has not designated any 2005 or 2006 American Eagle Coins or 2006 American Buffalo Coins as first strikes, nor do we track the order in which we mint such coins during their production. The United States Mint held a launch ceremony for the 2006 American Buffalo Gold Coin on June 20, 2006, two days before its release on June 22, at which two proof coins and two uncirculated coins were ceremonially struck. However, those coins were not individually identified and were put in regular inventory after the ceremony. The United States Mint did not hold any striking ceremonies for the 2005 or 2006 American Eagle Coins.

The United States Mint strives to produce coins of consistently high quality throughout the course of production. Our strict quality controls assure that coins of this caliber are produced from each die set throughout its useful life. Our manufacturing facilities use a die set as long as the quality of resulting coins meets United States Mint standards, and then replace the dies, continually changing sets throughout the production process. For bullion American Eagle and American Buffalo Coins, the United States Mint makes an average of about 6,000 coins from one die set. For proof versions of the 2006 American Buffalo Coins, the yield is an average of about 1,500 coins per die set. For proof versions of the American Eagle Coins, the yield is an average of about 300-500 coins per die set. This means that coins may be minted from new die sets at any point and at multiple times while production of a coin is ongoing, not just the first day or at the beginning of production. To put this in context, in 2005 the United States Mint produced approximately 356,500 one-ounce gold, 8,891,000 silver, and 6,300 one-ounce platinum American Eagle Bullion Coins.

American Eagle and American Buffalo Coins are not individually numbered and the United States Mint does not keep track of the order or date of minting of individual bullion or proof coins. The United States Mint begins production several weeks before these coins are scheduled to be released. By the release dates for 2005 and 2006 bullion coins, the United States Mint had already minted approximately 50% of the projected sales numbers for these coins. Any dates on shipping boxes containing uncirculated bullion coins sent to Authorized Purchasers are strictly for quality control and accounting purposes at the United States Mint at West Point. The date on the box represents the date that the box was packed, verified as 500 ounces and sealed, and the date of packaging does not necessarily correlate with the date of manufacture. The date on shipping labels and packing slips for proof coins, which are sent directly to United States Mint customers from our fulfillment center, is the date the item was packed and shipped by the fulfillment center. The other numbers on the shipping label and packing slip are used to track the order and for quality control.

I hope this helps clarify the misleading advertising for FIRST STRIKE COINS.  The US Mint does not track which coin is produced when and as such they tell me there is ABSOLUTELY NO WAY TO TELL IF A COIN IS A FIRST STRIKE OR NOT.