How do I create a new member in a Data Set?

If you leave new member file without modifying it, it won't be saved. This why you can't just use PGM=IEFBR14 with DSN=USER.LIBRARY(MEMBER),DISP=SHR. It will not be saved because it wasn't modified in any way. You need to use IEBGENER. You want to create data set without writing any data into it so you can use empty in-stream DD statement '//SYSUT1 DD *'. In such case end-of-file mark is written to member but it is enough to create it.

//JCLLIB05 JOB NOTIFY=&SYSUID,MSGLEVEL=(1,1)       
//COPYMEM  EXEC PGM=IEBGENER                       
//SYSPRINT DD SYSOUT=*                             
//SYSIN    DD DUMMY                                
//SYSUT1   DD *                                    
//SYSUT2   DD DSN=[Data set name]([Member name]),DISP=SHR