That lack of numbers indicates it was probably made by POTF-IZ during Task Force 10's 2007-2008 deployment. If you can share the picture of your other billboard/poster, I'd be curious to see what it is, as it might help narrow things down a bit. For now, here is how I'm dating your product without it having a sequence number:
Sometime during the surge, things got pretty busy, and a lot of PSYOP products were being reformatted into other mediums. If you look at that sequence number I posted above you see "HB" (Handbill). The same exact product might also be found in other formats (with "BB" for billboard, LF "leaflet", etc). [The other numbers reflect the country, year, target audience, and desired objectives]. Sometimes when dimensions change from one medium to another, an illustrator has to alter the product to make it fit the new format. When they have to also edit numbers that are embedded on a product it adds another step to the process. Product numbers fell off during the surge, around the time of TF10 running the POTF, and this trend continued until the end of OIF. Since I have a copy of virtually every single product made after TF10 left, I can reasonably determine it was made during their time or before.
Although not doctrinally correct, it was easier to simply skip publishing numbers on a product and instead have a database at a headquarters that listed all historical products. Great idea, in theory. These images were usually saved on an external hard drive. While this worked pretty well initially, hard drives eventually failed and some units took them home after a deployment. Almost all of those extensive databases are lost to history, save for a couple of units that printed bound books for their own historical documentation purposes (or to sell to help with fundraising for a dining out, NCO fund, etc)..
Sadly, the same is true with a lot of databases from OIF/OEF - countless SIGACTS, SITREPS, Operations Orders, and service records are already gone forever. For those ones that did get saved, that content is still susceptible to bit rot.