Is there an option to persist MQTT offline messages to disk?

This kind of thing is good to build in your own application, rather than the SDK, since everyone's going to have different desires for how this kind of thing might work. Have it store the QoS1 message to disk/database/etc before passing the message to the MQTT client, then remove the message from storage when the puback (acknowledgement from server) is received. When your application starts up, iterate over any stored messages and send them to the just-started MQTT client.

In the V1 SDK: https://github.com/aws/aws-iot-device-sdk-python
you can use the publishAsync():
https://github.com/aws/aws-iot-device-sdk-python/blob/0fb8d7859016386c0aa5dbd8e8aa07da8f187505/AWSIoTPythonSDK/MQTTLib.py#L630
and pass an ack callback to know when the server has acknowledged the message.

In the V2 SDK:
https://github.com/aws/aws-iot-device-sdk-python-v2
the publish() call returns a tuple, where the 1st item is a future that completes when the puback is received:
https://awslabs.github.io/aws-crt-python/api/mqtt.html#awscrt.mqtt.Connection.publish
so you'd use future.add_done_callback():
https://docs.python.org/3/library/concurrent.futures.html#concurrent.futures.Future.add_done_callback
to know when the server has acknowledged the message