how fast we can grab newly opened window object property

That sounds like it's pretty much impossible to answer.

I will vary depending on:

• The machine it's running on. It'll take longer on a slower, less powerful machine.
• What the background process you're waiting for is. Some things will take longer than other to happen. This time may vary as the app acquires more data. It may get faster as it loses/destroys data.

This is a "how long is a piece of string" question I think.

I sounds like you'd be better off using built in functionality, or building your own helper function, that waits for a configurable amount of time, checking if objects exists and/or their associated properties until you either get a match, or pass your timeout threshold.