The Franklin has NX-326 on her hull and as her registry, but she was stated to have been the first Warp 4 ship, which one would think would place her construction before Archer's NX-01.
My theory is that she *was* built before the NX-01, and had some other UESPA or Earth Starfleet hull designation, and was decommissioned and "mothballed" (at a location similar to the later Surplus Depot at Qualar II) along with a lot of other ships, possibly dozens, from that fleet, over time. At some point later (3-10 years after the formation of the Federation? - but shortly before the decommissioning of MACO, which would have taken time to negotiate and more time to actually wind down as a service), in an effort to quickly expand the number of available ships (because of a war, or to support a massive exploration effort, or... any number of possible reasons), the (Federation) Starfleet Corps of Engineers (or whatever the predecessor organization was - possibly just the Starfleet Engineering department) suggested pulling the ships that were still in good condition out of the depot, upgrading them as well as could be done quickly, and putting them back into service. 32 viable hulls received this treatment, and since seeing if this would work well was an experiment, they were designated NX-300 through NX-331.
Yes, I'm pulling most of these numbers out of my posterior and if you like the overall idea, feel free to adjust to taste.
And if you're wondering where ships 03-299 came from, my theory would be that some were other NX-Class ships that were under construction at the end of Enterprise, but many others were ships from the various home defense fleets of the new Federation worlds that were added to the Federation Starfleet, and that for a while that fleet looked very much like a hodge-podge with only hull markers and other livery binding them into the same fleet - and full integration took a loooong time for some (like the long lived Vulcans and their USS Intrepid that I presume operated under Starfleet only through the command structure of the subordinate Vulcan Space Command, explaining how they could be an all Vulcan crew but Spock was still regarded as the only Vulcan actually properly IN Starfleet.... )
Thoughts?
My theory is that she *was* built before the NX-01, and had some other UESPA or Earth Starfleet hull designation, and was decommissioned and "mothballed" (at a location similar to the later Surplus Depot at Qualar II) along with a lot of other ships, possibly dozens, from that fleet, over time. At some point later (3-10 years after the formation of the Federation? - but shortly before the decommissioning of MACO, which would have taken time to negotiate and more time to actually wind down as a service), in an effort to quickly expand the number of available ships (because of a war, or to support a massive exploration effort, or... any number of possible reasons), the (Federation) Starfleet Corps of Engineers (or whatever the predecessor organization was - possibly just the Starfleet Engineering department) suggested pulling the ships that were still in good condition out of the depot, upgrading them as well as could be done quickly, and putting them back into service. 32 viable hulls received this treatment, and since seeing if this would work well was an experiment, they were designated NX-300 through NX-331.
Yes, I'm pulling most of these numbers out of my posterior and if you like the overall idea, feel free to adjust to taste.

Thoughts?