Unless Ukraine has something that can knock down theater ballistic missiles the Ukrainian AA network will be targeted by a combination of tactical ballistic missile strike
Ballistic and even cruise missiles are fairly bad tool for SEAD. Not only they have a relatively long flight time to their target, they also are extremely dependable on very accurate intel, since the missiles don't have any ability to track mobile SAM targets. Only static radars and installations are truly vulnerable. However most of theater level
spotting and guidance level is mobile. There are many dozens of systems, most of them modified in the previous years,
plus new models, deployed as a part of various SAM brigades. These will be extremely hard to catch with the missiles. Note that while the destruction of large static radars will hurt (they mostly cover long-range spotting), it won't spell doom, since not only individual battalions can operate separately if required (this is not a completely centralized system ala Iraq), but also one has to count on the US providing intel using their AWACS and reconnaissance assets.
and SEAD by the Russian Army. Leaving Russia with superiority over the sky.
Russian Air force has little experience in SEAD. They also lack pretty much any coherent system and training for this kind of a task. Look at the orchestra of assets used by the Coalition in Iraq 1991. Multi-echelon reconnaissance, beyond the horizon guidance systems, entire squadrons of dedicated EW assets, a massive amount (1,200+) of strike and air superiority aircraft, including dedicated SEAD Wild Weasel units, heavy bomber squadrons with precision weaponry, stealth aircraft, hundreds of tankers and extremely efficient ground support network at the airfields, as well as a very sharpened doctrine and tactics at both squadron and individual pilot level.
Even with all the reforms since 2008, Russia has very little to show in this regard. They have a number of anti-radiation missiles, but they never had any dedicated SEAD units. For comparison, average annual flight time for fighter and strike pilots of the VKS is around 80 hours, with only some pilots getting close to 100 hours and many less than 60. On the other hand, American pilots of 35th and 37th TFWs (some of Air Force's most distinguished dedicated SEAD wings) often have 200+ annual hours
in SEAD training alone. Their EW is still mostly based around helicopter and ground-based assets, meant for covering own ground formations (makes sense as NATO doctrines never really revolved around ground SAM systems). Only a relatively small number of EW pods have been introduced for Su-34 and 30\35. Speaking of which, there are only ~120 Su-34 available (most effective Russian strike platform) and about 300 Su-30\35. There are also ~100 Su-24, but these are unlikely to be used for SEAD due to incompatibility with many newer systems. But this doesnt mean by all means that all of these aircraft will be simultaneously combat ready and that all of them will be deployed, leaving other theaters (including direct borders with NATO) without cover.
I know Ukraine had S-300s in the past but I'm not sure about their current capabilities.
Ukraine used to have ~60 battalions (x12 launchers) of S-300 alone, of course after decades of neglect there were only ~30% semi-operational in 2014. But many were brought back and even modified in the recent years. And there are dozens of other SAM battalions, including Buks, Tors, even modified Krugs and S-125 Pechoras. This represents considerably more than what Iraq had in 1991. This is a tough nut to crack.
The US probably doesn't have the resources to bolster SAM numbers so it would probably be another NATO aligned nation willing to ship them SAMs and trainers.
NATO in general has very limited SAM availability. Almost all systems are naval based. Standard NATO doctrines focus on aircraft based air dominance, and only recently some new SAM systems were developed for anti-missile defense, still in small numbers.
u/Styrdwolf