ArcGIS Sever from AWS Marketplace can't publish mosaic dataset image service by default. The document [1] says both ArcGIS GIS Server and ArcGIS Image Server are required to publish mosaic dataset.
Installation guide for ArcGIS Image Server is provided in [2].
Esri does not provide technical support for provisioning and configuring cloud infrastructure beyond what ArcGIS Enterprise deployment tooling creates and manages as part of its normal operations. For cloud platforms for which Esri does not provide specialized deployment tooling, support is limited to troubleshooting software-specific issues.