Realistically I think Britain would freak the hell out, those guys were huge on maintaining the European balance of power and a Großdeutschland throws said balance completely into whack. Historically, they opposed Russian designs on the basis that the Russians getting to realize their Pan-Slavic/Constantinopolitan ambitions would make them too strong and left Napoleon III to get rekt by the Germans because they still thought at the time that a stronger Prussia would be better for the BOP than a strong France, not realizing until it was too late that not only was N3 not the equal of N1 in either ability or ambition but that a united non-greater Germany was still a juggernaut with overwhelming potential. So they'd probably try to assemble a coalition out of anyone they can and bankroll efforts to dismantle this Greater Germany until either they went under, or it did, just as they had gone through seven coalitions to crush France's continent-dominating aspirations. Speaking of which, France isn't suicidal enough to start a fight with a unified Greater Germany on its lonesome even under Napoleon III, so ironically you'd have a surviving Second French Empire with Alsace-Lorraine becoming probably the other main partner in such a coalition with Britain in a hurry.
Thus you'd probably still get WW1 sometime in your early 20th century, with Britain + France leading one side and Großdeutschland leading the other. What the alliances look like is still up in the air, though. If Greater Germany has antagonized Russia, this alt-Entente has more or less the same chance the real one did. If Russia's on the German team (which would probably take this Greater Germany being as friendly to Pan-Slavism as it is to Pan-Germanism), then the alt-Entente had instead best pray the Americans elect a Wilson or FDR-tier '''''neutral''''' who's so friendly to them that he will wade into the fray even if American public opinion strongly opposes getting involved (and ideally a lot faster than they did in their respective world wars), otherwise I can't see how they're going to last past the first Christmas. (Ironically, TR might do, since he was gung-ho about attacking Germany IRL after the sinking of the RMS Lusitania. Just need him to never promise not to run again after 1904 and for a similar incident to happen in this timeline, I guess.)
Italy might also be pro-German depending on whether Großdeutschland gives them the Austrian territories they desired, though they aren't as important a factor as Russia. The reverse is true of the Ottomans, who I think would join the Entente (and indeed were traditionally a British ally) if Russia is pro-German, but again they aren't going to be as important.
The best possible outcome for Großdeutschland that I can think of, in which they manage to avoid a WW1 analogue entirely, is that they somehow strike a deal with the British to let them dominate the continent while giving Britain a completely free hand in maritime/colonial affairs, thereby securing a hopefully eternal or at least long-term peace between the two. But I'm not sure how feasible that would have been, Britain never liked the idea of a universal hegemon on the European continent, supposedly friendly or otherwise. And you don't even need a Wilhelm II-esque zero-charisma diplomatic disaster with lots of personal hangups to get antagonism toward such an arrangement going on the German side either - merely a leader who thinks 'wait, we're arguably the strongest country in Europe, who is Britain to tell us what we can't do?' (A notion that such a leader wouldn't even be unjustified to come up with, mind. Who in history has ever been satisfied with just being an implicit #2 when they really do have the power to seize moar of everything?)