No. It's impossible for every object to interact with every other object, due to the assertion by general relativity, that the universe can, and is, expanding faster than the speed of light.
I then assume that the universe initially was expanding at, or close to the speed of light, and that it immediately after the big bang was expanding faster than the speed of light.
Some of the particles/forms of energy that would have reached us are also bound to have been "held back or deflected", even in the young stages of the big bang, and are now at a distance at which they can never reach us. They could have been held back by for example a black hole.
Potentially, if the expansion of the universe at one point was so slow that gravity from every particle had time to propagate to every other particle, then yes - every particle and energy in the universe affects every other particle.
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