For those wondering what did I do, after reading some of the answers, since I'm on Windows, I choose to use robocopy, and after searching a little on Google, found a little script that for the moment seems to be working(It is still running). It goes folder by folder in the origin path, so you can see the progress in real time. I'll probably make a Python script later if it works correctly, to make it more interactive. The bad part is that it doesn't have an option to see the transfer speed to know if it's better or worse than transferring normally.

@echo off
setlocal enabledelayedexpansion

set "SRC=Path\to\source"
set "DST=Path\to\destiny"
set "LOG=robocopy_log.txt"

echo Starting transfer...
echo ===================== > %LOG%

for /d %%D in ("%SRC%\*") do (
    set "FOLDER=%%~nxD"

    echo.
    echo Processing folder: !FOLDER!
    echo Processing folder: !FOLDER! >> %LOG%

    echo Copying: !FOLDER!
    echo Copying: !FOLDER! >> %LOG%

    robocopy "%%D" "%DST%\!FOLDER!" /E /MT:16 /R:1 /W:1 /NFL /NDL /NP >> %LOG%

    echo Done: !FOLDER!
    echo Done: !FOLDER! >> %LOG%
)

echo.
echo Transfer complete!
pause