How could I know how many stitches to cast on for top down raglan sweater?

There is no simple answer, but it can be answered.

With the yarn and needles you are planning to use, make a test swatch at least 4" by 4" in the pattern or stitch you plan to use for the neck area. Count the number of stitches across and divide by 4 - that is your stitch per inch count. Just for example, let's say it turns out to be 7.

Then. do a sample cast on of let's say 20 inches.and work about 3 rows of stitches. Place that sample around the neck of the person getting the sweater - or measure it against the neckline of a garment the person wears. That tells you the neck line length.

Yes, you can use a tape measure, but, tapes do not have the same drape as worked yarn, so your measurement might be off.

Use the long cast on piece and the sample swatch to compute the number of stitches needed.

Let's say the neckline turns out to be 15 inches. Multiply 7 stitches by 15 inches and get 105 stitches. That is your cast on count.

Yes, this is a bit of work- maybe an hour or so, BUT, making a sweater- and it sounds as if you are not just knitting it, but designing it as well- takes a lot of time and effort. It would truly be a shame to put all of that labor into creating something special and have the finished results come out less than hoped for.

Do the preparation and you will like the result.

Also, TAKE NOTES.

Since this will be your own design, you are entitled to copyright the pattern. That means you could try to sell your design to the yarn company that makes the yarn you use, or to a magazine or a knitting book publisher, or even to a manufacturer. It is worth the few seconds it takes to jot the row/round number and the stitch count even if you only THINK that the only thing might be for you to make this sweater again. I save a bit of the yarn and note the needle size and material- sometimes it can matter if the needles are steel, aluminum, bamboo etc.

[I have made - didn't know I was designing...- original sweaters for myself and people I love for decades.

The definition of an expert is a person who has made all the possible mistakes (and presumably learned not to repeat the unproductive ones) in a particular field. I might not be an expert yet, but I am getting there...]

Top Down Raglan Sweater

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No-one would know how many to cast on without a pattern, the needle size and the yarn.