Advances in complex oxide heteroepitaxy have highlighted the enormous potential of utilizing strain engineering via lattice mismatch to control ferroelectricity in thin-film heterostructures. This approach, however, lacks the ability to produce large and continuously variable strain states, thus limiting the potential for designing and tuning the desired properties of ferroelectric films. Here, we observe and explore dynamic strain-induced ferroelectricity in SrTiO$_3$ by laminating freestanding oxide films onto a stretchable polymer substrate. Using a combination of scanning probe microscopy, optical second harmonic generation measurements, and atomistic modeling, we demonstrate robust room-temperature ferroelectricity in SrTiO$_3$ with 2.0% uniaxial tensile strain, corroborated by the notable features of 180{deg} ferroelectric domains and an extrapolated transition temperature of 400 K. Our work reveals the enormous potential of employing oxide membranes to create and enhance ferroelectricity in environmentally benign lead-free oxides, which hold great promise for applications ranging from non-volatile memories and microwave electronics.