As @a_horse commented , you will need to use the regex operator~ to use parenthesized expressions .
But there is more. I suggest:
SELECT *
FROM tbl
WHERE value ~ '^00[^0]'
^... ( ).
[^0]... ( ), , 0.
:
SELECT *
FROM tbl
WHERE value LIKE '00%'
AND value NOT LIKE '000%'
? LIKE , , . , LIKE.
, NOT LIKE '__0', LIKE '00%' , ( ) NOT LIKE '000'.
Postgres btree value LIKE '00%' value LIKE '00%' ( ), . Postgres , . :