Create a raster image with integer sequence in Google Earth Engine

I’d like to create an image with pixel values that are integer sequence 1,2,3,4…. . With pixel size equal to a MODIS pixel 500m and pixel align with MODIS as well. So that I can use a grouped reducer to do zonal statistics to count how many Landsat pixels (30m) are included in a MODIS pixel(500m). What I’ve tried to addressing this issue are:

1. to generate a grid with size equal to MODIS image resolution. WORKED but facing pixel alignment issues or projection issues which I will post for another question link. I assume by generating an image will be more straightforward to do zonal statistics than create a grid polygon in Arcmap then imported to GEE.
2. convert MODIS image to vector to create a pixel-to-polygon layer and use polygon ID to zonal. Failed. The converted pixel polygon is not corresponding to pixel in an image, somehow the algorithm turn two neighbor pixels as one single polygon even I set the eightConnected argument in reduceTovectors as false. This is not desired.