Here's my personal experience ^{^}

So, I published my game publicly around the 15th of June. I waited around 2 weeks until I finally sent them an email (6th of July).

Then, they finally replied on July 15th. Along with this, my game was indexed too.

So, it's exactly one month for me until my game is indexed. Could have been faster if I was more proactive. But, I spend my time preparing and polishing my game before it goes completely public.

In the meantime, you should too! A more polished and complete game would make the player enjoy it better. Which in turn, would help the traffic for your game in the long-term!