Could we use everyday at the beginning of the sentence?

For example:
Everyday I sunbathed on the beach and swam in the warm sea.

Yes. But it is two separate words when used this way.

It's one word as an adjective,
eg my everyday sweater.

Yes, but it's two words: "every day".
Here's a usage note from the Oxford dictionary:
"The adjective everyday, 'pertaining to every day, ordinary,' is correctly spelled as one word ( : carrying out their everyday activities), but the adverbial phrase every day, meaning 'each day,' is always spelled as two words ( : it rained every day)".