Hello,
We have a digital downloads store selling digital artwork. No, this is not one of the products that Google excludes in Google Merchant and is allowed. 
Right now Google is showing incorrect information for delivery and shipping.
What is the best method to set the delivery time to 0 and shipping cost to 0?
Hey @dcs-larina
You can configure the delivery information in Merchant Center using this doc. Make sure your Shopify setting for the product also says no shipping required.
You can configure the returns information in Merchant Center using this doc.
I’m not really seeing details in the two articles. I setup custom shipping as free, but didn’t see a way to specific delivery on the custom shipping option.
Please note that Google Shopping is generally a physical item only. While in some cases Google allows digital items such as software (for example microsoft word) most merchants trying to sell digital products eventually get disapproved.
This may also put your Google Ads account at risk of suspension.
So my advice, do not set it up, close down your Google Merchant Center account.
However, if you want to risk your business, simply setup zero shipping in Google Merchant Center shipping settings which has been shread by @ilanadavis
Again, my advice, do not proceed, you may regret the concequences.
Delivery isn’t as obvious as returns. You have to set everything to zero. As with everything Google, we provide the data and hope they use it, but ultimately it’s up to their algorithm what’s shown in search results.