As Ron mentioned in his answer, the "hotkey window" feature has got you covered.
After installing iTerm2, check that you have two profiles in the Profiles > Open Profiles
panel: one called "Default" and one called "hotkey window".
If you don't have the "Hotkey Window" profile listed in the profile settings:
- Open
iTerm2 > Preferences
and go to the Keys tab.
- Locate the hotkey window options in the bottom left of the Preferences dialog.
- Ensure that both the "Show/hide iTerm2 with a system-wide hotkey" and the "Hotkey toggles a dedicated window with profile" checkboxes are checked/marked. This should create the "Hotkey Window" profile for you automatically.
- Set the hotkey you want to use in the Input Box (I have it set to CRTL-^, just cuz it reminds me of the old Quake II times) and select
Hotkey Window
as the profile to show and hide in the dropdown list.
Enjoy!
This answer in the Ask Different community illustrates the above steps.
Additionally Nishchal Gautam asks, as a comment to Ron's answer, if you can hide apps from the command + tab
listing of apps running. Too bad I don't have enough reputation to place this response as a direct comment to the current answer, but here is the answer: iTerm2 supports this as part of it's "Advanced" options:

There's also an answer to that question in the Ask different community, to do it manually. Both options achieve the same, the former being the easy way.
Note: I'm just adding this new answer with the link for a more complete reference because, in comparison with Rob's answer, it states very clear that you need to tick both check boxes and select the "hotkey window" profile in the dropdown list at the bottom for the feature to fully enable the functionality - the link is a bit clearer than Ron, if you ask me: he does indeed mention everything you need to get going, but I had issues understanding the wording and had to further search why my settings weren't properly configured. That link made me realize that I overlooked the second checkbox. Silly me and my lame reading comprehension skills.
Note2: I just figured out that Ron's answer doesn't cover the most common case for when you don't have the profile already created. I've sent an edit request.