rasterio._err.CPLE_OutOfMemoryError: /io/gdal-3.6.4/frmts/mem/memdataset.cpp when trying to create a new large rasterfile

Question

I am trying to step by step save a lot of data in a single GeoTiff file but rasterio seems to fail right away when I try to open the file I want to write my data to due to my available RAM not being large enough to store the image all at once.

I am encountering this error:

rasterio._err.CPLE_OutOfMemoryError: /io/gdal-3.6.4/frmts/mem/memdataset.cpp, 1289: cannot allocate 1x40000000000 bytes

From this Code:

import numpy as np
import rasterio
from affine import Affine
from rasterio.profiles import Profile

target_transform = Affine(0.4999989733319868, 0.0, 371169.31953843555,
                          0.0, -0.49999725418315205, 6707833.49293414) # some transform
target_shape = (100000, 100000) # some large shape
target_profile = Profile(data={
        'driver': "COG",
        'count': '1',
        'nodata': np.NaN,
        'transform': target_transform,
        'crs': "EPSG:2154",
        'height': target_shape[0],
        'width': target_shape[1],
        'dtype': 'float32'
    })

with rasterio.open("test.tif", 'w', **target_profile) as dst: # This is where i get my error. 
    for ij, window in dst.block_windows(1):
        data = np.ones((1, window.height, window.width))
        dst.write(data, window=window)

I would like to be able to write to the file step by step without the need to have enough RAM to have it in memory all at once. I had hoped just windowed writing would fix this issue but rasterio seems to complain when I try to open a file that is potentially too large.

Are there possibly some parameters to the rasterio.open function that would solve this problem?