Can we use boost (^) functionality and then sort on that in results from query string?

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I have a field- Firstname and Lastname in my index. I have a query where if i type "Ra", i am able to get the results which start with "Ra" first as shown below using the boost (^) in query string on the Firstname field.
Ramanathan, Arumugam
Rajesh, Arumugam
Arumugam, Ranjith
Arumugam, Ramesh

But I also need these records to be sorted (i.e. Rajesh should come before Ramanathan) after boost so that i should finally get the results in below order which i am not able to achieve. This is because the sort function is being given priority over boost.
Rajesh, Arumugam
Ramanathan, Arumugam
Arumugam, Ramesh
Arumugam, Ranjith

Can someone help on this ?

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