I called it that this was going to happen about 2 months ago, slowly slowly more and more hit the 619 mark and are asking the same question OP is asking. The answer was generally do keys, and it still is because trading up can get you 15 crests a week, wow, one whole entire upgrade each week on gear that can be upgraded twice.
With 15 items minimum needing to be upgraded, give or take for the crafted slots and you need 30 WEEKS of ‘trading up’ to upgrade them all. Take away the additional weeks if you have spare crests and you may still need some 24 or so weeks from today.
Keys is still the answer, but players asking for this change, make M0 great again, give us solo content, it means keys is also not the answer because players like OP who may not have even done a key, is not going to be invited to the required M8 where the crests drop.
Blizzard should never have allowed players to solo content to get gear that is equivalent to an M6 that needs an M8 or mythic raiding to upgrade, because all it does it put players in a position that they now have to run normal raids to get experience for heroic raids to get experience for mythic raids, and even then, pugging into mythic raids is almost never going to happen.
And if they don’t want to raid, run low keys for experience so they can get into mid keys which will get them into high keys. But if they are a DPS, forget it, they will at this point in the season be running into players with 2.5-3K IO scores trying to get into the same keys, it will take them months to get to that point as a DPS, so for anyone trying to get past 619 iLVL, if they have only done so as Delves and don’t actually plan to do any other content, GG you hit your end game, go take a break or run some alts.