We can be sure Polonius arrives on stage earlier than his Second Quarto entry printed in the course of the dialogue, because of a line Polonius speaks later.  At line 230 Polonius will say to R and G, "You go to seek the Lord Hamlet."  Polonius must therefore hear Gertrude give them that instruction, which she will do beginning at line 037.  If Polonius doesn't hear that line 037, he will not know what he later says.  It confirms that Polonius must be present onstage now, or in this close vicinity in the dialogue.

We can be sure Polonius arrives on stage earlier than his Second Quarto entry printed in the course of the dialogue, because of a line Polonius speaks later.  At line 230 Polonius will say to R and G, "You go to seek the Lord Hamlet."  Polonius must therefore hear Gertrude give them that instruction, which she will do beginning at line 037.  If Polonius doesn't hear that line 037, he will not know what he later says.  It confirms that Polonius must be present onstage now, or in this close vicinity in the dialogue.