Is it possible to specify the exact time of JSS Inventory is polled?

Can you clarify what you're looking for here? I'm not sure I understand what is meant by "exact time of JSS Inventory polled" Do you mean the time a Mac submitted inventory??

The only way I know of is to manually do one along with a blank push, either from the web interface or API, and the result is "as soon as it's able to." The fastest is once per day otherwise.

Ah, I see. You mean specify the exact time when devices submit inventory to the JSS? If so, no, not really, and its by design. On the Mac side, even if you do, there is a random delay added to the policy that would do the inventory collection when its called by the LaunchDaemon. This is so in a large-ish environment you aren't DDOS'ing your JSS with all computers submitting inventory at once. So they will end up being staggered no matter what.
That said, you could always set up a policy scoped to all managed devices that would run between certain times using the client side limitations and use the Check-in trigger. In the policy the only payload would be Maintenance with the Update Inventory box checked. This only applies to Macs. I don't think there is any automated equivalent on the iOS side.

Edit: Never mind all the above since I'm seeing now you tagged this as an iOS question. There is no "policy engine" for iOS to do the above, so a blank push like @Emmert mentioned would be the only way I can think of, and its likely not recommended.

Can I ask though, what is the need to have a set time for your inventory collection?