As you say, Charlotte starts being friendly to Mr. Collins practically from the moment they meet, but the point about Charlotte is that she has her own kind of integrity. She makes absolutely sure that Elizabeth doesn't want him for herself before seriously going after him, which makes her speedy work all the more surprising! According to Ellen Moody's Chronology of P&P, Mr. Collins proposed to Elizabeth on November 27, and to Charlotte on November 30! Before the 27th, I think her behaviour was such that if Elizabeth had accepted Mr. Collins, afterwards he would have simply remembered Charlotte as "that nice Miss Lucas", but since Elizabeth didn't, it laid the groundwork for future efforts.