The solenoid will "insist on pulling in" as it is built.
There are solenoids which can be made to repell the armature from the core, but they need permanent(usually) magnets in the core to work.
You can get essentially the same result by adding a non ferrous* extension to the core so that when it travels inwards the extension moves outwards.
See diagrams below:
As typically implemented:
The above images are from this page.
If the coil end at the "pushing" end is open it will be relatively easy to insert something which can b pushed. If it is closed you may or may not be able to add a hole. Be careful not to drill through coild or wiring.
Many images from Google - most will be push solendoids - each is hot linked to a webpage.
Many for sale - some of these may LOOK like genuine push type but it is almost 100% certain that they will be pull type with an extension.