Can I run Edge0-35B-A3B-preview on an RTX 4060?

No

Even its smallest file (As published, 19.5 GB) is more than an RTX 4060 can hold (7.20 GB usable): it needs 3 of them.

Files and context on RTX 4060

Each file of Edge0-35B-A3B-preview (and of GGUF versions the site has analyzed), and how much context fits next to it, with the context cache in 16-bit or 8-bit.

Edge0-35B-A3B-preview on other hardware

Popular models that run on RTX 4060

Assumes 90% of the card's memory is usable and at least 4K tokens of context for one conversation, with the context cache in 16-bit unless noted. Fits leaves at least 20% of that memory for context; Tight leaves less.