Would this type of gambeson have made it into the first decade of the 14th century?

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What do you mean by "this type"? Gambesons with dags? Gambesons with collars? Gambesons with mittens? Gambesons with all of these features?

First, the reproduction looks too thin, and the attachment of the mittens is questionable.
The Soester Nequambuch from c.1315 show attached mittens still in use. The Manesse Codex from c, 1305 shows gamboissed collars.

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A gambeson needs to be 3-4 fingers thick if it is stuffed and quilted, or 1-2 fingers thick if it is layered and quilted.

I don't know about other people but I'm pretty sure from the shape of the gambeson that it uses a very modern cut for the body pieces, armscyes, and inset sleeves -- certainly not something that would have been seen in the early 14th century!