Considering a civilization that was here far before everything we know about, let's say around the time of Gilgamesh. Warm climate, almost no winters, near the ocean with enough rivers, and people being able to effectively work on the land, what kind of crops could they have? I was thinking main crop to be rice, then some vegetables as tomatoes, onions, cucumbers, carrots. But how about also grain? Or is it unrealistic to have them in the same area? Also corn and potatoes came to Europe from America, but would it be possible to have them on this continent a long time ago and vanished? I'm not sure about the combination of these crops, and what else to use.
Rice was almost certainly domesticated by 6000 years ago.
Early evidence for the use of wild O. rufipogon has been identified at Shangshan and Jiahu, both of which contained ceramic vessels tempered with rice chaff, dated between 8000-7000 BC.
If you have rice you probably have millet and if you understand the principles behind growing grains you can extrapolate to vegetables.
You do not really need all kinds of grain. We eat all kinds of stuff in these luxurious latter days but people historically had one main calorie crop which varied depending on region - generally wheat, or maize, or rice. Or bananas! I have read claims that bananas are the oldest domesticated plant. https://en.wikipedia.org/wiki/Banana
There are places where folks have switched up when a better crop has come along - for example the Irish switched to potatoes and the Italians to maize when these crops became available. Your ancients would probably have one or 2 main grains domesticated and would be relying on them.
The Americas didn't have any easy to domesticate crops, so at 6000BC you'll have to handwave a lot of things to make them available. Potatoes, Sweet Potatoes and corn were small, hard and not very nutritious. Tomatoes were poisonous except for mutant varieties. Gourds were used extensively to hold things, but they weren't grown for that purpose. There's a reason agriculture took so long to take hold in the Americas.
Mesopotamia, Indus Valley and China is where the action was happening.
Wheat, chickpeas, barley, peas, beans, flax and bitter vetch were all cultivated pre-7000BC.
7000BC emmer and einkorn wheat grown in Mesopotamia and Greece.
At some point before 6000BC olives were cultivated for their oil near or in Mesopotamia.
7000BC cultivation of wheat, sesame, barley, and eggplant. Some variety of beans were also grown.
6000BC first granary made.
6800BC Rice domesticated along Yellow River.
6000BC a number of crops from Indus Valley cultivated alongside rice.
Fruit trees were not cultivated for a long time. Growing fruit trees takes years of work and seeds did not produce the same quality of trees each time. Early farmers wouldn't want to bother with the years it took to produce fruit and the even longer time it would take to domestic them into something more useful than the wild variety. It wasn't until they learned how to graft varieties that were larger and more fruitful onto other trees, that domestication of fruit trees became common.
I second @Alexander they'd look different, bu-uuuut
Different, but the same
Yes, yes, the crops would be thinner, less "useful payload", different looks. But still same names! An apple is an apple is an apple! That it tastes not so well, is small as a wild apple, etc. is the second question. But for the purpose of the plot: it's an apple. Notice, however, no green apples. I mean, no apples that stay green when ripe. They are like from 1800s.
No Americas, no China
Of course, as you identified correctly, Americas were not yet discovered by Europeans, heck, there are no Europeans in our understanding yet.
So, no tomatos, no corn, no potatoes.
You might want to read up on the origins of wheat, rye, and other cores. Similarly for pigs and other cattle. (I vaguely remember China for pigs and hens.)
No exotics from Japan. No fruits from South-East Asia.
VERY few crops were domesticated by 6000BC
Other posts here mention the crops from the middle east and southeast asia that date from that era: wheat, barley, millet, sesame, soybeans, rice. Most of these were not yet quite in the form that we know them today.
From south america things like Cassava root.
From Austronesia, banana. (a very different banana, but the precursor)
The OP's "some vegetables as tomatoes, onions, cucumbers, carrots" simply did not exist as anything edible in that era.