Since you wrote that your brother travelled Germany alone and needs a work contract to obtain a visa, I would assume that he does not qualify for a residence card in Germany. In that case, the regular procedure is indeed to apply for a visa at a German consulate in Italy and to wait for that visa to move to Germany.
If your brother had moved to Germany with their EU citizen family member, he would be allowed to apply for a residence card directly (i.e. without going back to Italy to secure a visa). There are a couple of other exception to the need to secure a long-stay visa before entering the country: citizens from Australia, New Zealand, Israel, Japan, Canada, Korea and the US can apply for a residence permit directly and I believe the relevant authorities have the discretion to accept an application in exceptional cases but I wouldn’t count on it.
Either way, his status in Italy doesn’t really make a difference. It does however mean that his stay in Germany isn’t illegal as he has the right to visit Germany for 90 days. To avoid further problems down the line, I would recommend leaving Germany and going back to Italy before reaching the 90-day limit.