Yes, you should be able to. In essence, the state of the TPM is represented in the values of the PCRs (Platform Configuration Registers). Those are hash-extended through the boot process.

You can create a key or similar attribute which has an unlock policy based on those PCR values. If you play back the log of PCR write events from first principles (the log can be captured for debug purposes), you'll put the TPM into the same state and should be able to use anything protected by the respective policy.

For attestation, I presume you're thinking about sending an attested PCR quote - in that case, the TPM uses a non-extractable key to sign the current PCR states. As you can put the PCRs into the "correct" state, you'd be able to get a signed attestation the system is in that state.