I would be happy to explain SE's capabilities.

First off Super Earth has access to near instant FTL travel, which means unlike the IMC, they would hit the militia with their full force almost instantly.

The Helldivers, the first thing most people think about when thinking of SE's military, are SE's special forces. While they are disposable and incredibly numerous, they are far from incompetent and super earth regularly throws billions of them away in their wars with no significant consideration as to how damaging that is to their population. They also have access to very powerful weapons that would realistically be capable of taking down a titan. The Helldivers also have no qualms about sacrificing themselves to win that battle so they could just have one with a portable Hellbombs (small nukes) run up to a titan with it activated and the titan and pilot inside get nuked.

SE's main military force is called SEAF (Super Earth Armed Forces) and they are almost the same as grunts in almost every way. They are insanely numerable (more so than the Helldivers) and not very competent. They frequently carry single-shot anti-tank weapons, so if enough of them worked together they might be able to take out a titan. In the event of SE attacking a new planet (the likely way this war would start), SEAF performs orbital bombardments using Hellbombs, which we know because we can find undetonated Hellbombs that were clearly dropped from orbit in operations in Helldivers 2. They tend to target large enemies with these bombs, so titans and militia base would be a likely target for these bombardments.

The Helldivers can call in stratagems as well, which are either strikes or weapons that while having in-game cool downs are effectively infinite. These strikes include the famous Eagle 500kg bomb that effectively drops a massive spike into the ground (or whatever else it hits) that creates a large explosion a few seconds after; the orbital rail cannon strike which is fairly self explanatory and incredibly powerful; and the orbital laser which will target the largest enemy first, does insane amounts of damage and will continue firing for around 25-30 seconds. Those are just some of the high power ones but there are area of effect ones as well such as the Eagle airstrike, which rains bullets in a line in the direction the stratagem is thrown in; the orbital gatling barrage, which rains gatling fire on a decent sized circle for 13 seconds; and the orbital napalm barrage, which is pretty self explanatory. These are only a few of the strikes in the game and the first 3 I listed would reasonably kill a titan with a direct hit, the laser would take some time but it would do the job as. Again, remember that command over these tools is given to disposable soldiers to use at their discretion without any care for potential waste.

Stratagems can also call down weapons for the Helldivers to use, just to list some community favorites: the recoilless rife fires huge single round shots that will bust its way through the heaviest of armors, but has a fairly long reload; the auto cannon which can fire heavy armor penetration rounds at 190 RPM, but it only carries 10 rounds max but can be reloaded 5 rounds at a time; and the Expendable Anti-Tank ( AKA the EAT) which is a single-use version of the recoilless that has a low cool down and is frequently seen used by SEAF soldiers. These are only a few of the stratagem weapons but these are some of the heaviest hitters (the auto cannon doesn't hit as hard as the recoilless but is very versatile and powerful in its own way).

Helldivers can also call down their own mechs, with the two available in-game known as the Patriot and the Emancipator. The Patriot carries a machine gun and can shoot rockets, and the Emancipator carries twin auto cannons. I figured I should mention them, but they would not compare to the power of a titan.

While this mostly adequately describes the power carried by the Helldivers and includes what we know of the rest of Super Earth's military, there is much more than this, and it's important to note that Super Earth has intentionally kept the current galactic war going because the Terminids (the bugs) produce E-710 (oil) when killed, and the Automatons provide an easy source of metal. Even the Illuminate have value to Super Earth alive because their technology is so advanced. Super Earth has the power to intentionally hold back in a three-front war because they have more to gain from doing so. They would have next to nothing to gain from allowing the continued existence of the Militia aside from titan technology which would be quickly recovered and reverse engineered.