A lot of people seem to be confused about how to get 1600+ gearscore for the endgame dungeons. It's very possible, but not at all obvious.
The primary non-endgame source of gear for most slots is the daily rewards from Sword Coast Adventures. Log in, roll a die for your reward, and if you roll a 11-13, you get an unidentified item. If you're level 70, that unidentified item will be of blue quality and item level 111 or 115. Do this every day on every character and lots of such items are floating around. Today, you can buy such items for most slots for a few thousand AD each on the auction house.
Also important is that all such items come with enchantment slots. Add in a rank 5 enchantment (as mobs drop all over the place) for an extra 23 item level and you're at 1380 total item level before your shirt, pants, and artifact slots. You can add 40 to this pretty cheaply by upgrading all of those enchantments to rank 6.
For the shirt and pants slots, you'll need other options. There, you can turn to crafted items. When people use epic tools, they have a 60% chance of a rank 3 item and 40% chance of rank 2. Rank 3 has slightly higher stats, but more importantly, an enchantment slot. But rank 3 is also expensive.
So what do people do with the rank 2 items they craft? They sell them on the auction house at a discount--much less than the cost of the materials used to craft them. They're still epic items of item level 143, but have no enchantment slot. So buy a shirt and pants for about 50k each and that's another 286 item level. That gets you to 1666 with rank 5 enchantments, or 1706 with rank 6.
At this point, even assuming rank 6 enchantments, you've only spent about 300k to gear up a character. You can readily get that from daily invoking and leadership. Or if you're impatient, that's $6 by credit card to get to 1706 item level.
And we're still ignoring artifacts entirely. You get one free early on from a level 21 quest. You can also get them from The Vault of the Nine quest. If you complete this quest, you get an artifact that varies by your class. More importantly, all characters on your account can get this same artifact. Different characters of different classes can unlock different artifacts. If you have at least three characters of different classes, they can each get all three artifacts to fill your four artifact slots.
A brand new, rank 1 artifact is worth 26 item level. Once you upgrade to blue at level 30, it's worth 46. Purple at level 60 makes it worth 96. It takes 22,385 refinement points to get an artifact to rank 30. For comparison, it takes 311,185 to get to purple at rank 60; 3,847,635 for orange at rank 100; and 10,469,635 for the cap of rank 140. Now, getting to mythic at rank 140 is for whales. But rank 30 is not. One way to refine to there is a mere 21 rank 5 enchantments as mobs commonly drop in level 70 areas--or areas that scale your level down if you're level 70 yourself.
So let's ignore the higher ranks of artifacts and just go for blue. Four artifacts at 46 item level each makes 184 item level from artifacts. Add that in to what we've assumed above and you're at 1890 item level. That's all without setting foot in an epic dungeon, fighting any mobs in campaigns, or buying outlandishly expensive gear. That's well over the 1600 threshold to get you access to tier 1 dungeons, which offer you better gear to gear up for other content.