I don't really see why this is a safe bet, whoever sent signals first is going to be heard by the other party first*, and we have no reason to assume that we were first.
* assuming there's nothing "magical" going on like FTL signals etc
Personally I think our first encounter with aliens, if we ever have one, is going to be more similar to plants, bacteria, etc. It will be very underwhelming.
[0] (timestamped) https://www.youtube.com/watch?v=3vD4df_63wo&t=382s
If the Earth's entire history up until now is reduced to a single day, then our technological civilisation has only existed for the last few seconds before midnight. It seems unlikely that the civilisation next door also coincidentally appeared in the same few seconds.
Doesn't do much for sci-fi tho.