Not really, you can do it with 619 gear. As mentioned above, 619 is the end of Delves gear upgrade. Nothing wrong with that, if you really want to go further you can go Mythic + or Raid.
If you want to only play Solo, then it stops here. You can accumulate some crest and trade them but it’s not worth the time to be honest.
As you said, you are a solo player. But you can still make some group content if you can find the time. Puny mentioned good communities if you want some peaceful people to play with: Players Unable to Upgrade Delve Items - #7 by Punyelf-draenor