Odakyu Romance Car timetable

I'm planning a day trip to Hakone and I've met a bit of confusion in the planning process. For the Okadyu Romance Car Limited Express train between Shinjuku Station and Hakone-Yumoto Station, I am getting different timetables from both Google Maps and the Odakyu online booking page.

According to Google Maps, there is a train that departs from Shinjuku Station at 07:00 and arrives at Hakone Yumoto Station for 08:26am. Meanwhile, on the Odakyu page, the earliest train that I am getting results for is 07:37am with an arrival time of 09:22am.

Preferably, I would like to get the 07:00 train and maximise by day in Hakone. And I would also like to make an online reservation, however, there is no 07:00 train on the Odakyu website. But Google Maps says that it's an Odakyu Romance Car.... So, I don't know if I should just turn up before the 07:00 departure time and hope for the best or book for the slightly later train.

Btw, I'm not travelling during Golden Week and I will also be travelling on a Monday.

There are two different timetables:
- one applies to regular weekdays
- one applies to weekends and national holidays

The official timetables are here:
https://www.odakyu.jp/english/romancecar/timetable/