Greeks
The Greeks of classical antiquity idealized their Mycenaean ancestors and the Mycenaean period as a glorious era of heroes, closeness of the gods and material wealth. The Homeric Epics (i.e. Iliad and Odyssey) were especially and generally accepted as part of the Greek past and it was not until the 19th century that scholars began to question Homer's historicity. As part of the Mycenaean heritage that survived, the names of the gods and goddesses of Mycenaean Greece (e.g. Zeus, Poseidon and Hades) became major figures of the Olympian Pantheon of later antiquity.

Q: How did they believe their forebears lived ?
Mycenaean period as a glorious era of heroes, closeness of the gods and material wealth