Wikipedia said:
On 25 June 1656, Charles X Gustav signed an alliance with Brandenburg: the Treaty of Marienburg granted Greater Poland to Frederick William I in return for military aid. While the Brandenburgian elector was free of Swedish vassalage in Greater Poland[*], he remained a Swedish vassal for the Duchy of Prussia. Brandenburgian garrisons then replaced the Swedish ones in Greater Poland, who went to reinforce Charles X Gustav's army
*By greater Poland it's likely meant the Voivodeship of Kalisz and Poznań (more or less the later Posen)
How do we succeed in letting Brandernburg gain "Greater Poland".
I can see two different possibilities.
Brandenburg doesn't change side and the Swedes get a better peace; the result are a Swedish victory, Sweden gain Livonia, Courland, Ermland, Kulmerland, Marienburg and Royal Prussia, while Ducal Prussia becomes under Swedish overlordship. Greater Poland end up under Hohenzollern control, and outside Swedish, Imperial or Polish ovelordship. It simply becomes the (maybe Grand) Duchy of Posen.
The other possibility are that the Hohenzollern make a deal with Poland, where they gain Greater Poland for joining the Polish side. Greater Poland likely stay under Polish overlordship.
I personal find the first the most interesting. It has some interesting consequences, but at the same time very few large scale consequences outside Poland and Brandenburg, keeping the timeline very similar to our for decades. So let's go with it.
The Electors of Brandenburg are now vassal of both Sweden (Ducal Prussia) and the Empire (Brandenburg, Hinterpommer, Magdeburg, Berg, Markm and etc), but also a sovereign ruler in Posen. Sweden are stronger but not much more than OTL, Royal Prussia will likely be occupied by the Brandenburgians in the Scanian War, but they will leave it again, because of French dictate in the peace treaty.
Posen had a smaller population than Royal Prussia and was poorer, but it will be a much more prestigeous possession, because it is sovereign state. So Brandenburg-Prussia will become Brandenburg-Posen instead. So when Frederick I get his royal title it will likely be "king in Posen" rather than "king in Prussia".
After the Great Northen War the Hohenzollern will likely receive Royal Prussia, Kulmerland, Marienburg and Ermland plus sovereignty in these territories. Later it will all be raised to the kingdom of Posen. Poznan will likely serve the same purpose as Königsberg in OTL, a prestigeous city, where the Hohenzollern king are crowned. Of course with it better geographic placement, it may replace Berlin as the capital of the Hohenzollern domains (in fact this is very likely it had a bigger population than Berlin)
What would the cultural and linguistic impact be?
Even in OTL these areas was 30-40 German by 1918, they will likely be majority German in TTL. But even for the Slavic inhabitants much will change. These possession lies outside the HRE, as such the Hohenzollern are free to push a new state church down over the locals. They will likely keep the Brandenburg co-official status of Lutheranism and Calvinism mostly to avoid pissing off the Lutheran estates in their old domains. They will likely conmvert, mostly because the Catholic clergy are replaced with Protestants and Church domain confiscated. Of course they won't be "good" Protestant at first. But when the Pietist movement hit, we are going to see a interesting change. In OTL the Pietist translated the bible into the local languages of Masorians and Prussian Lithuanians. Here they will likely also make one to Kashubians and the Poles in Posen. The Pietist movement will likely transform the Slavs in the Posian domains into Slavic Germans or at very least a distinct alternative identity to the Catholic Poles.
Poznan as the new capital (if it end up that way) will likely grow fast with the infusion of the Hohenzollern adminstration and Protestant refugee, it will more or less turn into metropol over a few decades, and transforming into a important proto-industrial centre for the Hohenzollern. Berlin on the other hand will turn into a lesser version of Magdeburg rather than OTL metropol. It will be a transportation hub for the poor land of Mittelmark, but also as a stop between the fertile Altmark and Magdeburg and the political important Posen.