When a print queue is created?

Windows will always automatically scan the network for available printers.
That's of course, if you're sure you never connected it through USB cable.
In both cases, when Windows knows about it (drivers included in Windows), it will create the printer.
If Windows does NOT know about the drivers, it's either still there (if networked, but with a yellow exclamation mark), or not there at all.

Thanks for your reply.

My printer is a network printer, I access it via an IP.

How can I know when Windows discovered it and when Windows installed the driver?

The reason I asked this because I noted a HP Smart app is installed on my desktop while I only have this HP OfficeJet 250 printer installed on my laptop (not Desktop)

That would require me to go DEEP through the logs, and I have no auto-discover printer right now to test it with.
I suspect it IS logged in the event log. Problem is, the log isn't that big, and it's cyclic. If you wait too long, you can't find it anyway.
So if you must know, it's probably too late. If you think it's extremely important, set your application and system log size to a VERY large number

Thanks for your reply. I think the log can't keep for that long.

Also, I don't know why HP Envy has 2 devices there one with the word "Network" one without, but I never installed it twice, I am confused.

If I have two computers having the same printer installed, network discovery won't keep looping right? (I.e. My computer has HP Envy printer, then my computer discovered my other Computer at home also installed the same printer and add it as another device?)

Two printers, with one with the extra wording "Network", usually means, one time connected through USB, and one time discovered on the network.
If a printer is detected, it won't keep installing the same printer.