At the start Homelander has a significant range and AP advantage, not to mention the heat of his heat vision. Homelander effortlessly punched off Queen Maeve's head, and Kirito before his amps is only about 1.14 times stronger than her. Kirito does not want to get hit before he can activate his amps, and when Homelander throws his inevitable tantrum, he'll likely start with his heat vision while also rushing forward. Also keep in mind Homelander can fly while Kirito is just highly agile, giving Homelander the mobility advantage as well. Homelander definitely has a win-condition here.
Basically Homelander attacks first with his heat vision while Kirito defends against it by dodging or blocking. If Kirito gets hit he'll suffer serious damage and Homelander immediately gains the upper hand. If Kirito falls after getting hit Homelander will advance while still using heat vision on him and bear down on him. In this scenario Kirito likely dies.
Alternatively if Kirito dodges it, he has time to activate his first amp. At that point he either keeps dodging to activate his second in which case he will win, or he tries to fight with just the first amp, and eventually activates the second anyway. Ultimately I think the deciding factor is whether Kirito manages to avoid Homelander's first few attacks long enough to use either or both of his amps.
Kirito has experience dodging and blocking bullets and wide sweeping attacks to great effect. However, Homelander is attacking with an attack Kirito hasn't seen before, won't anticipate, and has the range of the bullets and the area of the wide sweeping strikes. I think it's most likely he'd be able to avoid it, with his skill and experience, combined with Homelander having no experience against anyone who could dodge or block his heat vision, but it's not a certainty.
TL;DR: Homelander will have the upper hand at first due to superior AP, Kirito needs to work hard to defend himself long enough to activate his amps, but his skill and experience mean he would likely succeed. Once the amps are activated AP will be evened out and Kirito can win via skill.
If it isn't then Kirito FRA
Counted. I really don't think it's a stomp when Homelander has a very real chance of killing or severely damaging Kirito before either amp comes into effect and before Kirito can cut Homelander's soft bits off, like his head.