I have to admit that this is quite early. The good news probably is that chances of it being colonized yet is unlikely which makes it easier to eradicate.
Please be sure the treatment is aggressive. Although chances are good your little one will culture pseudomonas again later in life, the longer you can keep it away the better.
If keeping it away isnt possible that at bay is important.
I do ?? since I was dx when I was 7 how they get a culture from a 5 week old......
Maybe the method isnt the most accurate also.
Hope others with little ones chime in.
HUGS & Welcome