It is sometimes depicted that the basic argument to read “the creation story” (Genesis 1) as a non literal story are modern science and the evolution theory. But I believe that the biggest problem with a literal view is in the text itself. More specific in the differences between the “creation stories” in Genesis 1 and 2.

Order of Gen 1

Vegetation created:

God said, “Let the land produce vegetation: plants yielding seeds
according to their kinds, and trees bearing fruit with seed in it
according to their kinds.” It was so. The land produced vegetation –
plants yielding seeds according to their kinds, and trees bearing
fruit with seed in it according to their kinds. God saw that it was
good. (1:11)

Human created:

Then God said, “Let us make humankind in our image, after our
likeness, so they may rule over the fish of the sea and the birds of
the air, over the cattle, and over all the earth, and over all the
creatures that move on the earth.” (1:26)

Order of Gen 2

No vegetation:

Now no shrub of the field had yet grown on the earth, and no plant of
the field had yet sprouted, for the Lord God had not caused it to rain
on the earth, and there was no man to cultivate the ground. (2:5)

Human created:

The Lord God formed the man from the soil of the ground and breathed
into his nostrils the breath of life, and the man became a living
being. (2:7)

Vegetation created:

The Lord God planted an orchard in the east, in Eden; and there he
placed the man he had formed. The Lord God made all kinds of trees
grow from the soil, every tree that was pleasing to look at and good
for food. (Now the tree of life and the tree of the knowledge of good
and evil were in the middle of the orchard.) (2:8-9)

All quotes are from the NET Bible.

Question

Is there a way to make a strong argument that both those stories are to be read literally (as if it was written by a modern historian)? How could those different accounts be merged?