Swapping a single bit inside a 40 bytes inputs fed to keccak256. Is it safe to assume no change in the first 20 bytes can result in the same hash? I have the following data (represented as hex from binary below) where the lower bytes is controlled by attacker in the second case :

0x00: 000000000000000000000000cf269986 ????????????????
0x10: da781407b0eeeac3ea79ac1c9d857d38 ?x???????y?????8
0x20: 00000000000000000000000000000000 ????????????????
0x30: 00000000000000000000000000000001 ????????????????
0x40: 00000000000000000000000000000000 ????????????????


which does 0x1350c327906a2da929ed2a625e133cdfc3aaa945d7540e93b1266293dd2c1d11.

0x00: 000000000000000000000000cf269986 ????????????????
0x10: da781407b0eeeac3ea79ac1c9d857d38 ?x???????y?????8
0x20: 00000000000000000000000000000000 ????????????????
0x30: 00000000000000000000000000000002 ????????????????
0x40: 00000000000000000000000000000000 ????????????????


which does 0xf11930e4cc6cdaaaa9da21243f512da3fba796ffa7c74870669af9cee3a06c0c. Because the use of 0x2 from 0x1 left shift a single bit by one (but both inputs keep the same length).

Even if the change is about a single byte, there’s no way to modify the first 20 bytes of the second case so the hash is equal to 0x1350c327906a2da929ed2a625e133cdfc3aaa945d7540e93b1266293dd2c1d11(the hash of first case) without requiring a computational power not available on the short term, right ?
There are no known attacks on SHA3 series that are faster than the generic attacks.

Your problem is the 2nd pre-image attack: given a message $m_1$ finding another message $m_2$ such that $m_1 \neq m_2$ and $Hash(m_1)=Hash(m_2)$. 

SHA3-256 has $2^{256}$ 2nd preimage resistance. 

Now, you only allow the attacker first 20-byte which is 160-bit of your data. The attacker must try to find the $m'$ if exist. He cannot brute-force the 160-bit space to execute the generic attack. That is not reachable, even 128-bit is not. 

The bitcoin miners' latest SHA-256 hash rate peak was $2^{66}$ hashes per second and $2^{83}$ per day from 108464285TH/s on 29/09/2019.

Another question is: does this 2nd pre-image exist? With a negligible probability, no!


  Even if the change is about a single byte,


We want the avalanche effect from the hash functions that is; a single bit flip should randomly flip the %50 percentage of output bits.

In general, if you want to find an attack into a good hash function you need some degree of freedom. What you are looking for is the reverse.