In short pulling their whole fleet, or even half their fleet for that matter, into Sol isn't a realistic option for the GTVA.
Simply to be effective a warship must be capable of independent operations for a couple of weeks at the least, probably closer to a month. It would be entirely possible to surge the whole fleet into the system and then have most of it leave again in a week. It simply wouldn't be wise
On the original subject:
The GTVA has to do two things. The first is eliminate the UEF as a fighting force. The second is to deplete or capture their stocks of supplies. A successful after frame requires uncontested control of the Sol spacelanes so that problem areas can be isolated and the interdependent network of colonies forced to submit to GTVA control or be starved into submission or otherwise deprived of needed resources.
This in turn means the GTVA needs to eliminate all combat spacecraft by destruction, depleting their supplies, or capturing them. We are not looking at a Middle East situation here. Spaceships are big and hard to keep operating, and it's already been established that the UEF has designed them as short-duration high-intensity combatants.
The UEF fleet will be fought to hurt it, rather than kill it, to place further stress on the logistics system. Logistics targets will be destroyed wherever practical. Once the UEF's space forces are out of beans, bullets, and black oil, there will be a mopping up period where they are attacked directly and either destroyed or captured.
After that, with the high ground lost forever, the UEF will inevitably surrender.