April 25 (Reuters) - Rubrik's shares rose nearly 21% in their debut on the New York Stock Exchange on Thursday, giving the Microsoft-backed cybersecurity firm a valuation of $6.77 billion.

The startup joins a list of companies that have seen strong debuts recently as initial public offerings bounce back on hopes of a soft landing for the economy, where inflation falls without a recession or big job losses.

Rubrik raised $752 million in its upsized IPO selling 23.5 million shares at $32 each, above the $28 to $31 range it had marketed earlier.

The company's IPO was underwritten by a syndicate of more than a dozen banks including Goldman Sachs, Barclays, Citigroup and Wells Fargo Securities. (Reporting by Niket Nishant in Bengaluru; Editing by Shounak Dasgupta)