In May 1937 King George VI announced that he was awarding the Order of the Thistle to his wife, Queen Elizabeth, who became the first female to be a Lady of the Order. (Queen Victoria, as the sovereign, had automatically become the Head of the Order)
Queen Elizabeth was installed in St Giles' Cathedral on 7 July 1937 during the ceremonial activities organised for the official coronation visit of the King and Queen to Edinburgh.
This video shows the King and Queen arriving and leaving the cathedral.
The only jewels which I have been able to identify for this ceremony are the coronation earrings and probably the Hanoverian pearls.
I have not found any information about the insignia given to Queen Elizabeth the Queen Mother initially. It is possible that she wore Queen Victoria's star - but that is just a guess on my part.
https://www.royalcollection.org.uk/collection/441235/star-of-the-order-of-the-thistle QEQM wore the sash of the Order for a formal Court held at Holyrood palace just prior to the ceremonial in the cathedral. On that occasion she wore the Oriental circlet and the "crown rubies".
It wasn't until the following year that HM was given her own star of the Order during the visit of the King and Queen to the Empire Exhibition in Glasgow in July 1938.
I don't have sufficient knowledge of Orders to recognise when QEQM might have worn the Order of the Thistle (except for the colour of the sash) so below are the only other two images I have found of HM wearing her Thistle insignia.