You gotta accept that you will die. Sooner or later you won't be able to endure any more AA fire while being chased by enemy planes. GAA moreso than bombers who can hide at high altitude and has better defensive fire. You'll be shooting at targets while under fire. Such is the life of a GAA pilot. You can mitigate AA fire by taking out the gun part of AA emplacements (triangles) ASAP. You'll need to keep flying and shooting and bombing until you get a feel of how much punishment can a given target in the tier take, and you'll become more effective by being able to move onto the next target faster. This applies to bombers too, but in terms of how many bombs and how dispersion might ruin things. Understanding the targets' durability and sectors' layout will be the key to successful attack plane play, GAA and bombers alike.
You'll wish you had these heavy planes at all when there are "heavy" sectors like Mining Plants or Military Bases in the pictures. LFs are often powerless against the former and the small ordnance load of the other two can only do so much. The Miltary Base appears to be easy for fighters because it's so hotly contested that there will be planes flying above. But if it's empty you'd wish you had an attacker to nail off the 80 pointer so you can kill the two ADAs and capture it. Also of note is the command center - you can't capture it on 3 fighter ADAs, but MRF can cover the rest easily with overwhelming firepower or ordnances.
Outside of forward airstrip, an attack plane is assured to have enough points to capture sectors through ground pounding alone - even the airbase, but under the assumption that no one else has been shot down over the sector and in the case of airbase, every single target outside of repair pad are needed for a capture through ground attack alone.
Like Trauglodyte said, this is the one case where rushing up the tiers is advisable and is recommended, especially for GAA. Luckily, you can sidetrack into T7 GAAs on both Germany and USSR through the Me 410 and I-220, respecctively, the former even lets you start the Me 265 somewhat upgraded, with engines and 30mms. Consider this option if you're already on those lines. The attack planes start to be able to do their job by that point, with powerful cannons and ordnances, with more speed to go around the map.
The bombers will manage in lower tiers, but the lack of hard targets and weaker bombs diminish their tactical value until around tier 7, where 3-sector maps stop appearing altogether giving you more sectors to go to. The bombers' ordnance load doesn't change much until the top tier where it truly become ridiculous, but they do go faster than GAAs overall and better at attacking
Maps with no "heavy" sectors such as all garrisons or garrisons+airfields will be disadvantageous to bombers due to overkilling soft targets and the targets worth less per bomb spent, whereas GAA's guns are well-suited to destroy the soft targets while ordnance can be reserved for armored targets or emergencies. In maps with many "heavy" sectors such as double mining plants, is where the bombers shine the most, being able to blow through all the hard targets in one bomb load, potentially capturing in a single pass without giving the enemy time to response.
Remember, the time a GAA spend dogfighting is time it is not working. Disengage where possible and concentrate on flipping sectors. The GAA not doing its job can be a direct contributor to team defeat because the sectors are not flipped back.
I had to re-grind GAAs on Asia, and the USSR low-mid tier isn't a fun prospect. You're too slow and your ordnance too few or too weak. It's not until the IL-8 or IL-10 where you are fast enough and has enough firepower to be truly effective. I sidetracked into Me 265 through the 410 and it served me well on missions that needed ground pounding, the Me 329 beyond it is surprisingly effective, and the German jets are better than the USSR ones in the environment that you need to compete with bombers with their superior speed taking you places faster. The USSR GAA jets (IL-40) has better HP and their guns are better at shooting off soft targets due to higher RoF and overheating less.
Low tier attack planes simply don't have what it takes to do their job well or even at all (The TSh-2 has no ordnance and can't even load ammo to improve fire chance), by the time you stop seeing 3 sector maps they are starting to matter in battles more. There is a reason why people complain and discourse on tier 10 bombers, after all...