Henry Bogdan (french historian) in La guerre de Trente Ans (Perrin), writes that Christian IV of Danemark was (as duke of Holstein) appointed President to the Lower Saxon Circle and charged of raising troops to defend it. He had full support of Brandenburg and Saxe-Weimar, received subsidies from England and Dutch Republic, and reinforcements from Bohemian exiles. Bogdan says he had 10.000 men in early 1625 but 25.000 in june.
Meanwhile, the Emperor had only Tilly's army left, who suffered desertions, and was threaten from all sides. That's why he accepted Wallenstein offer to raise 20.000 mercenaries and appoint him commander in chief in july the same year.