You can use the following scripts to know when the database was started.

select
to_char(logon_time,'Dy dd Mon HH24:MM:SS')
"Oracle Startup Time"
from
sys.v_$session
where
sid=1 -- sid=1 represents the PMON process
;

Here's an example of the output.

Oracle Startup Time
-------------------
Tue 20 Mar 07:03:24