So, this is an extremely complex question about which many large books have been and will continue to be written, but the answer is, essentially, yes.

The Latin script was descended largely from the Greek alphabet, which in turn was descended from the Phoenician script, which was ultimately descended from the Proto-Sinaitic script which was used approximately 3,800-3500 years ago.

The Cyrillic alphabet is substantially similar to, and a direct descendant from, the Greek alphabet, which was brought northwards from Greece through Bulgaria to Eastern Europe and Russia in the early centuries CE.

The Arabic alphabet was also descended from the Phoenician script via the Aramaic script. The Hebrew alphabet is similarly a descendant of Aramaic.

I would be remiss if I didn't note that there were numerous other scripts in use in the greater Mediterranean and Mesopotamian area during the first two millennia BCE - not just Egyptian, but also Sumerian and Assyrian cuneiform, Minoan writing (Linear A and B, and Cretan hieroglyphs), Ugaritic writing, and a number of others, all of which could, and very likely did, also contribute to the development and slow evolution of these scripts over the years. Some of these early scripts remain partially deciphered, or entirely undeciphered, so we need more information on them to speak more clearly as to where they do or do not fit in the evolutionary line.

All of this brings us back to the earliest common ancestors of these writing systems - Phoenician and Proto-Sinaitic. There are some intriguing links between Proto-Sinaitic and Egyptian hieroglyphics; in fact the Proto-Sinaitic script has been found in Egypt at a very early date (here is one abstract from a scholarly source: https://nelc.yale.edu/publications/two-early-alphabetic-inscriptions-wadi-el-hol-new-evidence-origin-alphabet-western - there are lots of sources available). Hieroglyphics, as you note, were explicitly pictographic in nature.

An example: the hieroglyph for "Ox" looks like a little ox head. The Proto-Sinaitic version looks kind of like a capital A on its side, with the point as the ox's nose, and two little horns on top. The Phoenician descendant of that letter looks pretty much exactly like a sideways "A." The Greeks and Romans simply turned the letter 90 degrees clockwise, and there you have your modern capital letter A. (Lowercase letters are a whole separate kettle of fish, and arrived on the scene much later.)

One thing I'd like to note: when looking for sources regarding the very early development of writing systems, it is more than usually important to critically and carefully judge the quality of your sources. There are a lot of pseudo-scientific sources surrounding some of the arguments being made. Also, sources on early writing are also affected by current political concerns - which alphabet was "first," and which people used which alphabets in which place at which time, are used as political evidence by some people even today in very real, very modern sociopolitical and religious contexts.