Can a purchased domain’s history affect its trust in Google?

A question from Dave Shuts, Yorkshire, England:
I bought a domain 7 months ago. The website I put on it still doesn’t show in the SERPs. Since 2000 it’s had different owners – used by a co. in Oz, it’s then served ads, then “for sale” with a company for 4ish years. Will it have trust issues in Google?

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