@ECHO OFF

SET FirstDate=2015-01-24

REM These indexes assume %DATE% is in format:
REM   Abr MM/DD/YYYY - ex. Sun 01/25/2015
SET TodayYear=%DATE:~10,4%
SET TodayMonth=%DATE:~4,2%
SET TodayDay=%DATE:~7,2%

REM Construct today's date to be in the same format as the FirstDate.
REM Since the format is a comparable string, it will evaluate date orders.
IF %TodayYear%-%TodayMonth%-%TodayDay% GTR %FirstDate% (
    ECHO Today is after the first date.
) ELSE (
    ECHO Today is on or before the first date.
)


and / or

@ECHO OFF
SETLOCAL ENABLEEXTENSIONS

REM -- 2 digit day
SET "_day=%DATE:~-10,2%" & REM day goes first (dd/mm/yyyy); if not, remove this line
SET "_day=%DATE:~-7,2%" & REM day goes second (mm/dd/yyyy); if not, remove this line
REM -- 2 digit month
SET "_month=%DATE:~-10,2%" & REM month goes first (mm/dd/yyyy); if not, remove this line
SET "_month=%DATE:~-7,2%" & REM month goes second (dd/mm/yyyy); if not, remove this line
REM -- 4 digit year
SET "_year=%DATE:~-10,4%" & REM year goes first (yyyy/##/##); if not, remove this line
SET "_year=%DATE:~-4%" & REM year goes last (##/##/yyyy); if not, remove this line

REM -- The variables below are set to year-month-day without separators (yyyymmdd)
SET "today=%_year%%_month%%_day%" & REM today's date based on your selections above
SET "compareDate=20180727" & REM the date you are comparing with today

REM -- Here's where the magic happens with comparing the two dates
IF %compareDate% LSS %today% ECHO The comparison date is in the past.
IF %compareDate% EQU %today% ECHO The comparison date is today.
IF %compareDate% GTR %today% ECHO The comparison date is in the future.
GOTO :EOF