From the oracle documentation https://docs.oracle.com/database/121/ADMIN/dba.htm#ADMIN11048 , here's what sysdba provide to your user:
Perform STARTUP and SHUTDOWN operations
ALTER DATABASE: open, mount, back up, or change character set
CREATE DATABASE
DROP DATABASE
CREATE SPFILE
ALTER DATABASE ARCHIVELOG
ALTER DATABASE RECOVER
Includes the RESTRICTED SESSION privilege
What you need to see your tables with your other user is either:
grant select on *normal_user*.table1 to *your_sysdba_user*
and repeat it for each table
or you can go bar open with
grant select any table to *your_sysdba_user*
but be advised that select any table include everything from everyone including data dictionary view which may be more than you truly wish to allow
I would assume that your sysdba user would be close to database god like sys so that would be ok but the disclaimer is there so you know