Google: rearranging the header tags do not affect ranking
A permutation of header tags on the page affects its ranking in Google. About this said the representative of the search John Mueller during a regular hangout for webmasters.
In other words, if the first page specified tag H2, then H1, some H3 tags, or two or more H1 – it doesn't matter for search engines.
"You will not see any changes in ranking, reversing the order of headings", — said Mueller.
Listen to his answer, starting at 5:40 of the video below:
About changes and the latest techniques in on-page SEO, including the use of title tags.