You can grow Cucamelons outdoors but it's best to start the Cucamelon plants indoors first and then transplant the Cucamelons outside when they begin growing.
You can then plant the Cucamelons outside in the soil after any danger of frost is gone which is around April or May depending on your location.
Keep the Cucamelons growing indoors until every bit of danger of frost is fully gone otherwise the frost will kill them.