Sleuthing this photo was pretty easy given the scoreboard, and most of what I want to talk about here isn’t the date of the game, so let’s get that out of the way first.
The Cubs linescore clearly says “ATLANTA/CUBS” and there are five score lines per league side. That immediately dates this to between 1966 and 1968, because the Braves began play in Atlanta in 1966 and in 1969, the leagues expanded to 12 teams each and the scoreboard added a sixth linescore.
Next clue: You might recall photos like this where there was Astroturf placed over the vacant center-field seating sections:
(And no, sorry, there’s not enough detail to sleuth that one, other than to say that it’s Tony Perez of the Reds at first base and Billy Williams running.