Basically you can do it (check if your esxi-management has correct IP, and try if routing works), but be very carefull. Someone else might try to do it in the same way as you, and take over control of your esxi-server. ESXi-firewall is not state-of-art, because it is probably not expected someone will deploy esxi to internet directly, without any protection (and I strongly discourage you from doing this)...
I personally have hw-firewall with vpn-server sitting between my esxi and internet, and my esxi-server I have one more extra NIC with IP from private address space for management interface. So first I have to connect to vpn-server running on HW-firewall, create VPN-connection, then I have access to esxi-console and management interface.
You could run vpn on VM (VMA) too, but it is not that safe, because if you shutdown that VM, then you have no access to esxi.
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If you found my answer useful please do *not* mark it as "correct" or "helpful". It is hard to pretend being noob with all those points! 😉