“I wonder which way I ought to go.” ~ Alice
There are quite a few ways to allow access to applications on your home network from the Internet. Port forwarding through your firewall is the easiest and most dangerous. A VPN is also an option that usually requires a separate machine and a client app on each device used for access. VPN setup can be a bit involved and speed can sometimes be an issue.
Access to Home Assistant itself can be accomplished with my preferred solution below. If you want to also access your Home Assistant devices through Google Home speakers, you must create an integration using Google Home Development Console. Home Assistant must be externally accessible with a hostname and SSL certificate. (A Cloudflare Tunnel provides this for you). A link to instructions is on the Links page.
Note: A no fuss Google Home, Alexa and Home Assistant integration can also by provided by Nabu Casa. The monthly subscription costs 6.50 USD. The annual subscription costs 65 USD. This price is excluding local sales tax. The subscription goes to support the team that helps to maintain and develop Home Assistant. They provide remote access and a certificate.
My choice is to use a free service called Cloudflare Tunnels. A link to instructions is on the Links page.
“Well, some go this way, and some go that way. But as for me, myself, personally, I prefer the short-cut.” ~ Cheshire Cat