Are backlinks from new domains useful?

If the new domains are spam-free, would they help us improve the ranking?

Short answer is it will not help. The only way in which it might help is if the domain is viral and either sends a lot of traffic through the link or if it's viral and has a lot of new links since it was registered

If you mean brand new or less than 6 months old, then no.

While they have no spam score, their metrics also are zero. On top of that, if the website isn’t yours, there’s no guarantee it won’t be spammed later on & become a low-quality backlink.

For tier 1, it’s best to go with good foundational links. Guest posts, outreach. Attempt to contact website owners with good metrics via their contact form and ask them/pay them for a backlink.

If you know that website will gain some authority in few months and Possibilities of getting spammed in future is less then go for it otherwise you can put that site in a future list and obtain backlink once it gained authority.