Thewliss was inspired to join the SNP at the age of seventeen following the 1997 Scottish devolution referendum. She was too young to vote in the referendum, but carried out an exit poll at a polling station as part of a Modern Studies project, which brought her into contact with representatives from Scottish political parties. Whilst still a student, she became involved in canvassing for the SNP at the 2003 Scottish Parliament election. A few months later, she was employed as a researcher for Bruce McFee MSP. By the time McFee had decided not to seek re-election in 2007, the party was looking for local election candidates. Thewliss agreed to stand for the Calton ward at the 2007 Glasgow City Council election which used a new multi-member ward system, and was one of 19 SNP candidates who gained seats previously held by Scottish Labour councillors under the previous single-member system. She was re-elected in 2012, but stood down as a councillor after being elected as MP for Glasgow Central at the 2015 general election.