Given that there was no hard number placed on the Reapers (but given the fact that there were probably thousands of them, if not hundreds of thousands given the fact that they were able to mount full offensives across /every/ populated star system in the MAss Effect galaxy), there's no possible way the Infinity would survive. Especially given the fact that the bulk (meaning the vast majority) of the Reaper fleet was also stationed around Earth...
Now if we just ignore numbers for a moment, let's focus on the weapons of the Reapers. Those giant red energy lines? Not actually pure energy, but streams of hyper-accelerated metal that ripped through the most advanced starships of the Mass Effect universe like they were made of paper. Given the UNSC (and Covenant) don't have Forerunner grade armor on their ships, well, you're looking at Infinity lasting maybe a few rounds with /one/ Reaper. And that isn't taking into account the thousands of Oculus fighters a single Reaper can deploy, all of which have far more manuverability and firepower than any currently displayed UNSC or Covenant starship, or Phaetons.
So even if the Infinity could somehow survive and take down one Reaper, it would still find itself dealing with thousands of superior fighter craft in large enough numbers that the Infinity's defenses would simply be overwhelmed.
Yeah, sorry kiddo, but your fanfiction is bad and you should feel bad.
The Reaper main gun is calculated as being equivalent to something around 400 kilotons of TNT at a high end. The strongest weapon in Mass Effect aside from the Reapers are Dreadnought mass drivers, which hit with the force of around 32 kilotons of TNT; they can explicitly obliterate almost any other ship in the setting, again aside from a Reaper.
32 kilotons of TNT is half
of the force expenditure of an under-powered UNSC Frigate MAC from the pre-war era, the weakest MAC shot there is. The ability to destroy any Mass Effect ship is not impressive.
Meanwhile, the UNSC Infinity's shields can comfortably survive a direct ramming of a Covenant RCS Armored Carrier, splitting it in two, without any negligible effect on the shields, despite causing the Covenant ship to explode along its plasma lines. That is several megatons of force there. It can also then survive the ensuing space battle with the Covenant fleet, again without much concern. All told it would have tanked numerous megatons of force. Its armor can also survive an impact with an asteroid; it causes the asteroid to crack on impact, and while the ship took damage on the interior, it on the whole survived without major damage. It has an armor thickness of 4.9 meters of Titanium A-3, ONI's newest and most durable hull metal.
Its MAC guns, of which it has 4 of the newest type, can pierce the hull of the Mantle's Approach, something the SMAC network and UNSC defense fleet failed to do. The SMAC weapons hit with the force of 51.6 gigatons of force for every shot they make. To explain what that means, 51.6 gigatons is 51,600,000,000 kilotons. A Reaper would have to fire its main gun around 129,000,000 (million) times to achieve the same level of damage.
The Infinity MAC weapon succeeded where the ODP grid failed and did damage to a Forerunner ship.
It is also armed with the following
Tens of thousands of missiles of varying yields, at least 8 megaton grade nukes and more. The Occulas fighter swarm can be matched by human pilots; the Infinity also has a pulse laser grid designed to snipe small fighter craft as they approach. They can hold an Occulus swarm off for a time, depending on the size of the swarm.
The Infinity will lose to the whole Reaper fleet, but a single Reaper would be a cake walk for it.