Creating a GeoTIFF with 3 large matrices (Latitude, Longitude, Data) [satellite images]

Dear all,

I am trying to create a GeoTIFF from 3 matrices, each of 2000x2048. Let's call them:

Lat = 2000x2048

Lon = 2000x2048

Data = 2000x2048

Now, being the coordinates not equally spaced accross the scene, I cannot use the approach where xmin xmax ymin ymax define the 4 corners.

I can do that, but when I export the file to a GeoTIFF, this is wrongly georeferenced, resulting in something "flat" like this (assuming x and y axis had coordinates):

What I am after is exactly what geoshow does. For example I can obtain the image below from:

geoshow(Lat,Lon,Data,'DisplayType', 'surface') 
colormap jet, clim([250 320]), colorbar;

And this is what I get:

Now, how can I create something like this, that can be exported as a GeoTIFF?

*Please note, I tried to create meshgrids but unsurprisingsly I get the following error:

Requested 4096000x4096000 (125000.0GB) array exceeds maximum array size preference (13.9GB). This might cause MATLAB to become
unresponsive.

Any help would be much appreciated!