Enabling OpenSSL on EC2 instance (free tier) without restarting server

Enabling OpenSSL on EC2 instance (free tier) without restarting server

I am currently trying to install openssl on my ec2 server so that I can
get rid of this particular error:
stream_socket_client(): SSL operation failed with code 1. OpenSSL Error
messages: error:14094410:SSL routines:func(148):reason(1040)
After doing some research I found out that I would need to enable
something in my php.ini file, however, I cannot enable anything that
relates to OpenSSL where I would need to make an adjustment like so:
from ;extension=php_openssl.dll to extension=php_openssl.dll
Thats when I realised that I need to install an extension for my php.ini
file to have that extension for me to enable it, however I do not know how
to install OpenSSL on my ec2 instance server without resetting anything
(my url addresses for my webservices would change otherwise upon reset).