Hi Jasonsone,
You need to set the Particle Emiter to Start, e.g., “-10” [frames]
Then the timeline to “-10” frames. (Or more !)
Render out from frame zero and as far as you need to get your result.
Tip. You can “Bake” the particles. IF done this, the time line can be set back to zero.
I have made a little one minute clip for you. The MoGraph suggestion is optional. :o) But perhaps with some more adjustments in the random Effector…
https://www.amazon.com/clouddrive/share/p8JT6youUD5Ne6Iq84SvBTwzdhFaidfqgXyqJEOCDuK?ref_=cd_ph_share_link_copy
You can download the clip if you like.
Let me know if there is any other question.
All the best