Regulation of adhesion is a ubiquitous feature of living cells, observed during processes such as motility, antigen recognition, or rigidity sensing. At the molecular scale, a myriad of mechanisms are necessary to recruit and activate the essential proteins, whereas at the cellular scale, efficient regulation of adhesion relies on the cell's ability to adapt its global shape. To understand the role of shape remodeling during adhesion, we use a synthetic biology approach to design a minimal experimental model, starting with a limited number of building blocks. We assemble cytoskeletal vesicles whose size, reduced volume, and cytoskeletal contractility can be independently tuned. We show that these cytoskeletal vesicles can sustain strong adhesion to solid substrates only if the actin cortex is actively remodeled significantly. When the cytoskeletal vesicles are deformed under hypertonic osmotic pressure, they develop a crumpled geometry with deformations. In the presence of molecular motors, these deformations are dynamic in nature, and the excess membrane area generated thereby can be used to gain adhesion energy. The cytoskeletal vesicles are able to attach to the rigid glass surfaces even under strong adhesive forces just like the cortex-free vesicles. The balance of deformability and adhesion strength is identified to be key to enable cytoskeletal vesicles to adhere to solid substrates.