This is just three years into the cease fire, I would imagine that the US government would seize interest into the wormhole project and look into weaponizing it for use against ECON.
The USAF would take funding and staff away from Cochrane's "Project: Phoenix" to devote more resources to the wormhole program
The Department of Defense begins planning for, "Operation: Archangel"...breaking the cease fire by using the wormholes to deploy Army Groups into the heart of ECON territory and preempt remaining ECON strategic sites.
2058: "Operation: Archangel" is a smashing success, ECON was still years away from anything comparable and was caught completely flatfooted as the US didn't telegraph force deployments to any contested territory.
With ECON completely surrendering, the wormholes fall to joint DoD/NASA control...on the military side they simplify logistics enabling cheaper occupation of ECON territory and more efficient aid distribution to the European Hegemony, NASA side is mostly propaganda missions (with a side of research) to the planets.
When NASA makes contact with Vulcan, the DoD realizes they are on the wrong side of a "starship gap", Cochrane is asked to comeback to work with unlimited funding and better facilities, NX-01 enters service 50 years early...and under USAF flag.
Politically the world has to accept American primacy and dialogue between the US and European Hegemony to reform the UN...transforms into the "United States of Terra", being built out of the US governmental system as a new primary tier...
United States of Terra -> USA -> States -> Counties
...the 'UST' would at founding consist of the USA, European Hegemony, ASEAN, and former ECON territory which was broken into two blocs after US occupation, Commonwealth of Independent States & Shanghai Cooperation Organization
Earth in this timeline would not be constrained by Vulcan oversight, by 2151 NASA and the USAF have parted joint operations for the most part. NASA uses the wormholes almost exclusively for exploration, while the USAF (now United States Aerospace Force) operates almost exclusively ships for territorial defense.
NASA does have it's own ships, but very few...and purely tailored for cosmic research. The DoD does still rely on wormholes for primarily the Army and force projection purposes...USAF specific use is generally limited to Pararescue.
The transporter jamming radiation would be a welcome surprise in time, and attempts would be made to reproduce the particles more cheaply for defensive and military purposes.
I would imagine that once the Terrans learn of the Iconian civilization and the parallels to their Gateways, NASA would stop 'boldly going" and would begin to operate far more meekly, while the military focuses on uparming the starfleet
And considering that real life 1960's proposals under USAF Project: Orion packed the firepower of a Galaxy Class Starship into an 87 Meter package...
....not hard to make ships that'd make Borg Cubes flee in terror, using 22nd century technology and antimatter...so long as you have the right mindset