Nordwestblock, Germani, and Grimm's law

In the Wikipedia article on the NWB one reads the following:

"Kuhn noted that since [PIE] /b/ was very rare, and since this PIE /b/, via Grimm's law, is the only source of regularly inherited /p/'s in words in Germanic languages, the many words with /p/'s which do occur must have some other language as source."

In cybalist message 65652, one reads: "the Grimm sound shift ... took place, judging from placenames in W Germany and the Netherlands,
no earlier than the 1st cent. BCE."

It seems to me that the Germanization of the NWB took place after the Grimm sound shift. otherwise the /p/ words and toponyms would also have been subject to it. Which means that the incoming Germani already spoke a language with the familiar "Germanic" consonants. If this shift occured "no earlier than the 1rst c. BCE" then the invasion and Germanization of the area took place still later. There are problems with this. Many linguists believe that Grimm much antedates 100 BCE And this is in line with the Wikipedia notion that the NWB area west of Jastorf was "Germanized" (post-Grimm) before 100 BCE:

"In the final centuries BCE, areas formerly occupied by the Elp culture emerge as the probably Germanic Harpstedt culture west[6] of the Germanic Jastorf culture" But Harpstedt-Nienburg succeeds Elp a little earlier than 500 BCE...

Wikipedia also notes that nothing has yet been finally decided, that discussion is still possible.