Solenoid Alternative?
Solenoids are as available in Egypt as they are here in the US.  DigiKey, Mouser, Farnell, and many others ship worldwide, including to Egypt.  If I needed to buy solenoids, I'd be buying them from the same places you can also buy them from.  Nobody buys electronic components from physical stores anymore.  The entire world is accessible at the other end of the internet.

1 inch is a fairly long travel.  A solenoid is basically a electromagnet with a core that can move.  It is difficult to make them so that the ratio of force at the start and end of travel is not huge.  The longer the travel, the harder this is.  For long travels, it can sometimes make sense to use a solenoid with shorter travel and a mechanical linkage that gives higher travel at the expense of less force.

Simple solenoids aren't that hard to make yourself.  Find two iron plugs, the right kind of nails or bolts can work.  Find or make a cardboard or paper tube they just fit in, and glue one of them so that it is fixed.  Wrap a bunch of wire around the outside of the tube.  When current flows, the movable plug will be attracted to the fixed plug.  However, getting this to work over 1 inch travel with reasonable force will be difficult.

Go to a local junkyard and see if you can salvage some starter solenoids.  Those are really relays implemented was solenoids.  Old Fords used to have them mounted on the side of the engine compartment where they were easy to remove.  I still have a photographic cable release built around one of those from many years ago.

One alternative to a solenoid is some kind of geared-down motor.  Hobby servo motor units can have 1 inch travel with the right arm.  However, those are going to cost a lot more than solenoids.

I think in the end your best bet is to do a careful internet search to find the product that does what you want and order it.  Even if a local physical store had it, it would probably be more expensive there anyway.