This is not possible.
As you mention, you will have a route (or a few) to get out of your network and you can see the outbound public IP address for there.
This may be only one of the many addresses allocated to a company. In particular, this outbound IP address may not be the one you would use to access publicly facing services (in a larger company this is very likely).
The non technical way could be via an ARIN / WHOIS search. The information you will find in there is as up to date as the network admins made it to be.
Then you can try to check the services you know about (www, ftp, ...) and may find an IP address which may or may not be one your company is an owner of (the web site may be hosted elsewhere for instance)
Except for asking the network admins there is not reliable way.