The gate to source voltage in a nMOSFET is vertical. Then how can it attract the electrons in the n region because the electric field associated with it is vertical and does not apply to those electrons.
In a MOSFET the gate to source voltage attracts minority carriers from the substrate and induces a conducting channel between the source and drain contacts via the field effect. The channel can contain electrons (called an nMOSFET or nMOS), or holes (called a pMOSFET or pMOS), opposite in type to the substrate (minority carries which wereattracted by the gate voltage and collected on top of the substrate to create the conducting channel. So, after the formation of the conducting channel, the application of a second bias (between the source and the drain) is responsible for the currents across the channel.
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In order to induce a channel in an nMOSFET, a potential is applied between the gate and source. If you look at the MOSFET structure, the gate and source are not vertical (gate and substrate are vertical). The electric field across gate and source therefore does not need to be vertical and can thus affect source electrons causing them to populate the channel.
The minority carrier concentration is low and it's gathering from substrate is slow process, so the main source of the carrier in channel is injection from source. The source-gate and source-drain voltages are making non-uniform potential on the gate dielectric, so the channel start to appear from the source and traveling towards the drain when you open the transistor.
You can read a book from Janis Tsividis about this process in more detail or watch his course on Coursera.
You should go through CHAPTER 3: THE THREE-TERMINAL MOS STRUCTURE of the book "Operation and Modeling of the MOS Transistor" by Yannis Tsividis and Colin McAndrew. They have explained it very well. The electron primarily come from source. Because of the depletion capacitance in substrate the surface potential has some finite value for a finite gate potential which helps to get electrons from source (for NMOS).