Computing devices that perform hardware rooted attestation are described, as are methods for use therewith, wherein such devices include a system integrated TPM (e.g., a firmware-based TPM), with m boot chain components loaded and executed prior to the system integrated TPM. Between powering-up of a device and the system integrated TPM being loaded and executed, seed morphing is performed for n=0 to m. This involves an nth encryption seed (ESn) being morphed into an n+1th encryption seed (ESn+1), under control of an nth boot chain component, by extending the nth encryption seed (ESn) with a measurement of the n+1th boot chain component to thereby generate the n+1th encryption seed (ESn+1). In a similar manner, an nth identity seed (ISn) is morphed into an n+1th identity seed (ISn+1). Such techniques establish trust in the system integrated TPM despite it not being the first component loaded and executed after powering-up.