Hello again, dear Zsuzsi17.
In that map (of your link) for JR Shinagawa Station, the difference in level is not well highlighted.
Better maps are available.
- JR East: Guide map for Shinagawa Station https://www.jreast.co.jp/e/stations/e788.html
- JR Central: Maps of station layouts https://global.jr-central.co.jp/en/info/station/
Anyway, you go up from the platform (probably for Tracks 11 and 12) to the concourse, pass through the Shinkansen South Transfer Gate, and go down to the Shinkansen platform for Tracks 23 and 24.
According to JR guidance on the poster in Shinagawa Station's concourse,
which is shown in Google Street View (as of February 2018),
the track for Tokaido Line trains running for Kawasaki is Track 12.
One elevator between Tracks 11 and 12
connects the platform and the concourse,
and its doors open at the concourse's south end
(= left end in the station maps).
You get off the elevator,
turn to the right, walk through the pathway,
and find on your left the Shinkansen South Transfer Gate.
Then, you pass through the transfer gate,
take the nearby elevator down for Tracks 23 and 24, and reach the platform.
- Google Street View
(1) Around the elevator between Tracks 11 and 12, on the platform: https://email@example.com,139.7394576,2a,90y,179.15h,1...
(2) Around the same elevator, on the concourse: https://firstname.lastname@example.org,139.739465,2a,75y,179.15h,10...
When your Shinkansen train arrives,
this elevator is close to Car Number 2, the second from the train's head,
which is among the cars for passengers going without seat reservation,
where seats are secured on the first-come, first-served basis.
On the supposition that you travel with a JR Ordinary Class ticket or pass,
I recommend you reserve your seat
in Car Number 4, 5, 6 or 7 of a Nozomi train, or
in Car Number 6 or 7 of a Hikari train.
(A Japan Rail Pass does not let you have Nozomi train rides.)
Any train in service on the Tokaido Shinkansen is composed of 16 cars;
Cars Numbers 6 to 8 are Green Cars,
where a Green Car ticket or Green Class pass is required.
So, if your seat is reserved in a car beyond these Green Cars,
it may be uneasy to get there quickly.
Shinkansen trains make literally brief stops.
When you have reserved your seat,
it is better to reach the platform at least 5 minutes in advance
(of your Shinkansen train's scheduled departure time)
and wait at the position for your train car. 1 stop from platform 1 in Shimbashi .
The departure track is Track 1 in Shimbashi Station.
Shinagawa is the next station for your train to make a stop,
which means you basically do not have to make room,
until the doors open at Shinagawa,
for other passengers getting on or off the train.
(On the Yamanote Line, between the two stations is Hamamatsucho Station,
which is a major transfer station for travelers using Haneda Airport.) We will be walking to Shimbashi from the B Tokyo Shimbashi.
It is about 500 meters to walk
from your hotel to the Karasumori Gate of Shimbashi Station.
(When a taxi goes smoothly to the Karasumori Entrance,
your taxi fare is estimated at around 500 yen per car.)
- Google Maps: Suggested walking route: https://www.google.co.jp/maps/dir/35.6674949,139.7534266/35.6660001,13...
You pass through the Karasumori Gate,
take the nearby elevator up for Tracks 1 and 2, and reach the platform.
Then, you get into the front half of your train,
which is, when the train arrives at Track 12 in Shinagawa Station,
closer to the elevator for the concourse.