How quickly does lateral flow show infection?

[MonsterKidz]

Does anyone have any insights into how quickly infection shows up on lateral flows?

Background is family went to a large indoor event yesterday, several hundred people indoors, precautions were in place, masks/negative LF before hand etc.

Said family member wants to visit me today. They have done a lateral flow today - negative. My question is how quickly do lateral flows show infection?

It’s very unlikely they’d be transmitting already from yesterday.

I think about day three or four with my DH and day 2 for me.

The incubation period of covid can be up to 12 days or longer although it's usually quicker for most people. But there is no specific time - they could have caught it yesterday and not become infectious until next week, or it could happen sooner.

So the point of people claiming that everyone in attendance had a negative lateral flow is pretty redundant then…