Hydrogels for organogenesis support organogenesis from mammalian cells, including human cells. The hydrogels contain a branched polyalkylene glycol functionalized with adhesion ligand peptides, such as integrin peptides and ECM peptides. In some forms, the hybrid hydrogels include a network of crosslinked branched synthetic polymers including a branched polyalkylene oxide polymer and a thiolated extracellular matrix polymer, preferably hyaluronic acid. In some forms, the synthetic hydrogels contain a branched polyalkylene glycol functionalized with GFOGER, RGD, YIGSR; and one or more ECM peptides, such as peptide(s) having affinity to fibronectin and/or peptide(s) having affinity to collagen and laminin. In some forms, the synthetic hydrogels possess desirable properties (e.g., a swelling ratio of ≤1.5 and/or a stiffness of ≤150 Pa) that allow the formation of perfusable vascular models in microfluidic devices. Also provided are methods of making the hydrogels and methods of using the hydrogels for organogenesis.