Heterostructures comprised of various atomically-thin van der Waals materials have proven to be highly flexible platforms for realizing novel quantum phenomena. In particular, twisted bilayer graphene with rotational mismatch of ~1.1° has emerged as an exciting new platform for investigating strongly correlated electronic phases owing to the unique degrees of freedom it offers – including tunability by electrostatic doping – and for the tantalizing possibility that the superconductivity it exhibits may be mediated by an unconventional all-electronic pairing mechanism. In order to realize more flexible control of the superconductivity, we demonstrate the ability to tune the correlated phases both with a transverse displacement field and by applying hydrostatic pressure. The latter is especially powerful as it provides direct control over the strength of correlations within a single device at a fixed twist angle. We show that for a device with 1.27° twist angle – in which correlated phases are otherwise absent – application of pressure drives emergent superconducting and correlated insulating states for both hole- and electron-type carriers, with record high Tc of the superconductor of over 3 K.