Assuming that you’re referring to “pulling information out of your ass”, you could try: “Pulling facts out of thin air” or “making it up on the go”. Getting more creative with it: “unscripted intellect”, “on the spot expertise”.

A real gentleman would probably say “conjecture” or “unfounded information”, but a less explicit word is “nonsense”

Somebody is trying to send a spicey work email lmao

Rectally sourced figure

Malarkey Nonsense Fabrication

An “ad hoc solution”?

Pulled out of thin air

Wingging it.

deus ex machina

i’m just spitballing here… i’m thinking perhaps… maybe… does this resonate… have you considered… from another perspective… possibly… informed opinion… its likely… in the ballpark of… something like…

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Amateur hour

Cut from whole cloth

Hexbear argument.

Colonjecture.