adamjd ,
Are you building this survey in EX or CX?
I am more familiar with CX but I imagine the approach is similar in EX. Also, it can be done, but this is not a beginner's project. I would recommend starting by reading up on Workflows (specifically the section on scheduled workflows) and Longitudinal Surveys. If you have the start date as an embedded data field I can imagine a Workflow that recognizes the date as past "today's date" and then it sends the survey.
WORKFLOWS: https://www.qualtrics.com/support/survey-platform/actions-module/setting-up-actions/
LONGITUDINAL SURVEYS: https://www.qualtrics.com/support/survey-platform/common-use-cases-rc/pulling-data-into-a-second-survey-longitudinal-surveys/
These are just a few ideas...do you have access to a TAM? They could probably map this out for you, or do it for you.
If you don't have access to a TAM, research the above links and see if that sparks any ideas based on your scenario. Check back with me and I'll guide you as best as I can based on your reply.

@ThomasW_IronMountain,
Thanks for your suggestions. I'm using Design XM, and we do not have access to a TAM. I'm pretty comfortable with more advanced project types, but in this case I'm not seeing an obvious way to do what I am envisioning.
For example, like you mentioned I had considered setting up a workflow (scheduled to run every day), with a condition to compare the embedded field for start date to today's date and if X days have passed then the task will be to distribute the survey via email to that contact using an individual link.
Unfortunately, it appears that conditions can only be added to event-based workflows, not scheduled workflows.
Another option I considered was to use contact list sampling. I could add a calculated date to each contact that indicates the date when their survey email should be sent out. Then draw a sample from my contact list that includes up to 100% of the contacts (so no limit) but applies a condition that the date to send the survey out is within the past 0 days (i.e., today). I would then then have a scheduled workflow resample this sample each day and distribute the survey to the resulting sampled contacts. This doesn't appear possible from what I've tried, since I don't see a task option for resampling a contact list in the available scheduled workflow options, or an option in the workflow to email survey links to a sample of a contact list.
Maybe there are other workarounds I'm not thinking of, or possibly things I have missed.

You can setup automation to add contacts to the 360 project based on certain metadata parameters and schedule the distribution accordingly.

https://www.qualtrics.com/support/employee-experience/creating-360-project/participants-tab-360/importing-evaluators-from-the-global-directory-360/

adamjd
You can use segments to do this, like you can add the dates in the format mm/dd/yyyy of their start date and create a segment as mentioned below. Use this segment within survey distribution automation and run it after the segment is hit refresh for the day. It will auto-filter the contacts.
Create it separately for 30,90,180 days as required and create multiple survey distribution automation for the same.
Hope it helps!

Deepak
Thank you for suggesting segments. This is exactly what I needed!
Very simple approach to what seemed like a complex problem. It just requires also adding an embedded field to the contacts to reflect the particular contact list that I want to limit these segments to (rather then the entire contact directory), and then including that field in the conditions when creating segment.