Q:

insert date in MMM YYYY format

Is it possible to enter date in format MMM YYYY while creating a table like "Jan 2020".

A:

Never store formatted date values in a database. Really. NEVER.
Instead, format date values as users retrieve them (in the SELECT clause) or even later (in the client code or reporting tool). If you have data coming into your system in a certain format, parse it to into a strongly-typed date or datetime value at the earliest possible moment.
With that in mind, instead of a varchar column to store values like Jan 2020,  you want a Date column. This gives you a real (complete) date value, where if you only care about the month and year you always use the first day of the month.
Thus, instead of Jan 2020 you would use 20200101 in the INSERT or UPDATE statement, and Sql Server would efficiently store a binary value.
Now you can use the FORMAT() function to get Jan 2020 back again, if you need it:
FORMAT( MyColumn, 'MMM yyyy')

The advantages here are the ability to use these values correctly in an index, do date math (DATEDIFF(), DATEADD(), etc), letting the database ensure you have real date values, and many more.

A:

Just saying... MMM yyyy will indeed convert to a date.  However, it will assume the 1st
Example
select try_convert(date,'Apr 2020')

Returns
2020-04-01

Furthermore, inserting a MMM yyyy string into a DATE column works as well
Declare @YourTable table (SomeDate date)
Insert Into @YourTable values
('Apr 2020')

Select * from @YourTable

Results
SomeDate
2020-04-01

