First lets make some test data. A 3x4 raster with no coordinate system. R will place this on a unit square. We'll also fake up some lat-long rasters:
r = raster(matrix(1:12, 3,4))
latitude = raster(matrix(rep(c(seq(34, 37,len=3)),4),ncol=4))
longitude = raster(matrix(rep(seq(10,23,length=4),3),ncol=4, byrow=TRUE))

Now we get the values from longitude and latitude:
vlong = values(longitude)
vlat = values(latitude)
and work out the cell size. In longitude that's the difference between the first two values in the raster, and in latitude its the difference between the values in the first and the "1 + number of columns" value:
xcell = diff(vlong[1:2])
ycell = diff(vlat[c(1,1+ncol(latitude))])
xcell
# [1] 4.333333
ycell
# [1] 1.5
Now set the extent of r to the min/max lat/long values plus or minus half a cell size in the right direction:
extent(r) = c(min(vlong)-xcell/2, max(vlong)+xcell/2, min(vlat)-ycell/2, max(vlat)+ycell/2)
print(r)
# class : RasterLayer
# dimensions : 3, 4, 12 (nrow, ncol, ncell)
# resolution : 4.333333, 1.5 (x, y)
# extent : 7.833333, 25.16667, 33.25, 37.75 (xmin, xmax, ymin, ymax)
Now we can test this by plotting the raster then adding the points referred to by corresponding points in the lat-long rasters:
> plot(r)
> points(longitude[], latitude[])

which looks dead on. If this doesn't work for you then possibly your lat and long values aren't equally spaced.
Thank you for your time
– um675 Oct 15 '20 at 15:25plot(values(long), values(lat))look like (if those are the lat-long raster)? A grid? Edit your question and put the plot there. – Spacedman Oct 15 '20 at 17:43