1 week into your ewe with little milk and what I have to offer might still be helpful. Any mammal's milk production is based on supply and demand, Mother Nature is very wise. The more that babies suck, the right amount of milk is produced and the right type of milk is consumed. Think about you or your wife and perhaps the children you have and breast fed.
The first milk that a mammal produces is colustrum. It's thick, important and isn't procuded in large quantities. It's like liquid gold because it's value has to do with antibody reservoirs. In humans; mother's milk comes into full production within 3 days. Any mammal, even sheep, have the some biology, full milk production doesn't happen immediately. It is a process.
If the lambs are warm and showing no signs of distress (not a raimbow style of posture) then all is well. Young ewes often don't have big bags yet their teets are very effcient. Milking a young ewe can be the most effective way to increase her milk production as she figures out mothering.
If you have a handful of sheep, as I do then this is an easy way to help with new lambs. If you have a large number of sheep then this would not be time affective for you. Perhaps others can shed more light than me.
Let us know your outcome.