

You can claim on the basis of being British subjects officially domiciled in the colonies that joined Confederation.
You will need baptismal certificates rather than birth certificates as Nova Scotia did not begin civil registration of births until 1908 but the provincial archives will lead you to religious archives that can help.








I would look at the FAQ on finding n documentation in the subreddit.
Family Search and Ancestry will help find Census records, birth certificates and baptismal records (for periods before civil registration which came quite late in several provinces).
Once you know where and when your Canadian ancestors were born, you will be in a good place to get a baptismal record from the appropriate provincial archives.
For this, it’s unlikely that you’ll need a lawyer.
However, if you’re looking for legal expertise, the two most experienced in citizenship by descent (practising in BC and Quebec) were guests on this recent Borderlines Podcast.