It can, and anyone who suggests it can't is questioning the process by which God created and manages the Earthly world.
Genesis 1:20 to 1:27 suggests animals came before humans. Genesis 2:18 tp 2:20 suggests humans came before animals. Genesis 4:15 suggests there were other humans in the land of Nod who were not direct bloodline to Adam and Eve.
Meanwhile, the Big Bang Theory was proposed by a Jesuit Priest (and Physicist and Astronomer), Georges Lemaître, and was ridiculed as "Genesis masquerading as science" by the scientists of the day.
Because you claim that those passages "suggest" contradictions doesn't make your assertion true. It may very well mean that you have an agenda to deconstruct the Scriptures, can't read without applying a biased template, or you are just trying to be argumentative.
I'm going to assume that you are the latter. In the case of suggesting a contradiction, perhaps you should try examining the narrative styles. In Chapter 1, we are given exact order and specific actions in very specific time frame. In Chapter 2, we are not even viewing the Creation, rather we are looking at the conditions and events that necessitated providing Adam with a suitable partner. That is, it is unsubstantiated eisegesis to say that the phrase "Out of the ground" indicates order, time and action. Especially when only a few sentences before we are given these details in the appropriate literary style. If anything, this is a confirmation that the animals presented before Adam were of the original six day creation (1:24) and not brought in from somewhere afar (or from water, or magic pixie dust).
Now in terms of that purely unsubstantiated assertion that there were other humans in Nod not of the bloodline (direct or not is immaterial) of Adam and Eve is easily explained by the statements of the historian Josephus that A&E had at least 33 sons and 23 daughters. Surely they married among themselves and produced offspring of their own.
Meanwhile, the Big Bang Theory was proposed by a Jesuit Priest
So what? Ptolemy had great credentials as a mathematician, astronomer, geographer and astrologer. Does that make him right? I don't get your point. Thousands of years theologians great and small say six-day creation. One dude gets caught up in the cosmology of the age and instantly the Biblical narrative is wrong.
It does not SUGGEST this, it says so
20And God said, Let the waters bring forth abundantly the moving creature that hath life, and fowl that may fly above the earth in the open firmament of heaven.
21And God created great whales, and every living creature that moveth, which the waters brought forth abundantly, after their kind, and every winged fowl after his kind: and God saw that it was good.
22And God blessed them, saying, Be fruitful, and multiply, and fill the waters in the seas, and let fowl multiply in the earth.
23And the evening and the morning were the fifth day.
24And God said, Let the earth bring forth the living creature after his kind, cattle, and creeping thing, and beast of the earth after his kind: and it was so.
25And God made the beast of the earth after his kind, and cattle after their kind, and every thing that creepeth upon the earth after his kind: and God saw that it was good.
26And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth.
27So God created man in his own image, in the image of God created he him; male and female created he them.
Genesis 2:18 tp 2:20 suggests humans came before animals.
18And the LORD God said, It is not good that the man should be alone; I will make him an help meet for him.
19And out of the ground the LORD God formed every beast of the field, and every fowl of the air; and brought them unto Adam to see what he would call them: and whatsoever Adam called every living creature, that was the name thereof.
The above verse describes how God created them, not when. It does not say "and then..."
20And Adam gave names to all cattle, and to the fowl of the air, and to every beast of the field; but for Adam there was not found an help meet for him.
Genesis 4:15 suggests there were other humans in the land of Nod who were not direct bloodline to Adam and Eve.
You are looking at this through the eyes of today. At the start, mankind was very long lived, almost 1000 years. Adam and Eve would have and did have very many children. Where ever Cain went, there would have been more than ample time for more to follow.
It can, and anyone who suggests it can't is questioning the process by which God created and manages the Earthly world.
It can not. the Creation is described clearly in Genesis. Anyone who says it can is calling the Word of God, in Genesis, a lie.