He accepts Shinji’s proximity (if Kaworu wouldn’t want it, he hadn’t done that kind of smile at him and he hadn’t invited him to spend time together)
I don’t know if it may be understood as “love at first sight” from Kaworu’s side; he felt attraction to Shinji because of his pure heart and his pure feelings towards him. But I think it is from Shinji’s side: Kaworu is attractive and people tend to pay attention to appearance, next to personality. And Kaworu’s dialogue “I have born to meet you”, it isn’t just empty words: he says that to Shinji after Shinji has talked about how his lifestyle is monotonous and lonely until he met Kaworu. I think Kaworu feels empathy since he understands how a lifestyle that way is.
Probably, Kaworu identifies with Shinji, so he wants to change Shinji’s point of view (giving Shinji a new opportunity to live and to get know how important is to everybody or watching over Shinji’s happiness like he has probably done in other dimensions). Apart from that, in semi-canon and no canon games, you can get the idea that Kaworu is always around, thinking a way to secure Shinji’s happiness at any cost, even risking his own happiness), even taking the risk of his plans fail.
I say that because, in my opinion, when Kaworu realizes that isn’t Adam there but Lilith, he thinks about his only two options: killing Lilith and all her children just as it has been planned (and probably staying alone for the rest of eternity since Rei-Lilith would never wake up without Shinji and, without his original body, Kaworu wouldn’t giving birth more angels), or dying and giving the opportunity of living to Lilins. And taking into account which is the worst fear to Kaworu, it’s obvious what decision he would take.