Child of 4 years having cavity is a clear sign of Early childhood Decay. Cavities are just manifestation of a bigger issue which is majorly inadequate home Hygiene...brushing method....feeding habits .. diet and most importantly no regular dental check-up visits preferably with a Pediatric dentist ( child dental specialist). Unfortunately, only paste change is not the answer. More importantly, kid who has cavities needs full coverage with High fluoride( 1000-1500 ppm of F) to minimise progression. A kids toothpaste has either 0 or kidodent and pedifluor has 500 ppm Of F only.
Next Steps
You don't have to search any tooth paste. Just start with your own regular toothpaste. 4 year old usually develop habits of spitting so ingestion won't be an issue. They might not like in beginning but then they get used to it. Make brushing interesting for them. There are good YouTube videos for it.
Health Tips
Most importantly, once the pandemic crisis is over...visit a certified Pediatric Dentist who can guide you for each and every step for cavity free mouth during childhood and adolescents. Prevention is always better than treatment...that should be the motto always. Best wishes.