Hi and welcome to the forum!
As with most things there are several ways to do this. I assume the ceiling is the same height as the connecting room. If so then you could just select the floor, right click and select Elevate but that will only work if the Kitchen floor is already separate from the rest of the room.
Assuming that it is not separate already, then the correct way to do it would be to ADD another Location for the Kitchen (Settings/ Building Locations) and set the Floor Level for the new location, to the height that the top surface of the floor is above zero (ground or terrain). In other words, the thickness of the Ground Floor (normally 1' or 300mm) plus the height of the Kitchen floor above the ground floor. Your image shows 3 steps so if they were each 6" or 150mm, then the Floor Level for the Kitchen would be 1'+1'6" (2'6") or 300mm+450mm (750mm). Enter this figure for the new 'Kitchen' Location Floor Level. This will now be the base for the Kitchen. Anything that you place in the Kitchen that sits on the floor (such as the cupboards) will insert at 2'6" or 750mm. If you do not do this and insert the furnishings on the Kitchen location then you will have to right click and elevate everthing.
Now you are ready to insert the floor. Make sure you have the new Kitchen location selected. Select the floor tool, but click the little arrow on the right of the floor icon and choose 'Floor by Picking Points'. This will allow you to draw the floor in a simlar way to which you draw the walls. Do not join the last side when you draw it - instead right click and select Finish - it will join it autmatically. You should be able to see the ground floor walls faintly, so you can trace them with the floor tool. Draw it with the 'cut outs' for the two sets of steps (ie draw the shape of the top surface). Don't worry about getting the sizes to exact, you can drag the edges later to make them correct. If you can see underneath this floor then just select it, go to Properties and change the thickness.
You can now insert the steps. Technically they should be inserted on the ground floor as they go up, but you could insert them on the Kitchen level and right click Elevate but use a minus to lower them.
Next you can switch to the Kitchen location again and insert your cabinets etc and they should all sit on the new floor. If you insert them with the Ground Floor selected they will be half buried by the Kitchen floor
There are a few little catches with this situation. If your ceiling is a different height then you may want to ask again how to do that. Any windows and door entered on the ground floor may have to be elevated in the Kitchen area to maintain their height in relation to the Kitchen floor.
I hope you could follow all of that. If anything is not clear just ask.
Allan