This question is not as easy to answer as it seems. Many teams default to two extreme options:
As you can expect neither is a good approach. In the first approach, you risk wasting lots of time on writing automated tests which would have little to no value.
In the second approach, you risk either having a big number of issues or spending lots of time and money on manual testing afterwards.
As always there's no right or wrong way here, however, there're some heuristics that can help you with this decision. I have created this mind map as a place to start: https://xmind.works/share/eZRBam34