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Gentle reminder that TVA Loki and Sacred Timeline Loki only diverged after most of the events in The Avengers had already happened. The Loki we see in Thor 1 and Avengers is actually BOTH Lokis.
Also, consider that Loki and Thor are 1500 years old (according to Thor). To keep the math simple, let's say that the events in Doomsday happen in 2027. That means the split would have happened 15 years earlier, in 2012. 15 years is only 1% of their lifetimes. TVA Loki and Thor were on the same timeline for 99% of their lives (at least from Thor's perspective — we don't know how or if Loki is experiencing time in the tree). It's only the events of the last 15 years that TVA Loki missed out on, and even then he knows exactly what happened during that time. Add in the fact that TVA Loki's timeline was destroyed right after it was created, which to my mind means that Sacred Timeline Thor is TVA Loki's next-of-kin. Thor and TVA Loki are most definitely NOT strangers. They're just brothers with some catching up to do.