I can't offer much concrete as I live in Singapore so don't transit.

However, assuming you to have to clear immigration, to pick up a checked bag, if there are no visa requirements for your nationality, you do need to do an electronic arrival card then you'll get through immigration really quickly and there is no need generally to queue for customs, so you can be out of the customs hall within twenty minutes or so of de-planing.

Arrival card:

https://eservices.ica.gov.sg/sgarrivalcard/

Scoot fly into T1 and SQ out of T2. Its about a ten minute walk landside between the two.

If you don't have a checked bag, my understanding is you can go straight to the SQ transfer desk airside. Its easy to get from T1 to T2 airside.

This may assist:

Connecting from Scoot to SQ at Changi - tight turnaround