I have a devops project with two teams operating on two-week sprints. I'd like to offset the sprints by a week and thus need separate iterations e.g.
Team A sprint 1 start 2020-10-01; Team A sprint 2 start 2020-10-15
Team B sprint 1 start 2020-10-08; Team B sprint 2 start 2020-10-22
Can anyone tell me if this is even possible and if so, how I achieve it.
Reading the Azure docs would suggest it is possible, but I can't quite work it out. I can see how I can select a different sprint from Team A's sprint dates but I don't see how I can create a separate (new) sprint date sequence 1 offset by one week.
You can absolutely do this. You can easily configure multiple teams in a single Azure DevOps project, and each team can have separate iteration hierarchies to organize sprints under.
While you may not create an additional "root" iteration node, there's nothing that prevents you from creating two child nodes, representing the product iteration default backlog for each team, with child nodes further underneath for each individual team sprint. This is, in fact, the recommended way to handle large organizations who use the One Project, Many Teams approach.
Example with the dates you mentioned: