Making a connection with the Divine to fulfill material desires while also making spiritual progress is the core concept of Puja. In ancient times, spiritual seekers who reached advanced levels of meditation and union with the cosmos (yoga) were able to control the energies within and around them as they wished to get the desired object or event manifest.
When such rishis just gave a mere blessing or curse through their words, their tapas was such that these things used to occur as it is. What happens here is that the energy they accumulated arranges things in the cosmos so that the event they wish or utter occurs. Many of them devoted their lives to the public good. And several others mostly spent life in solitude in the bliss of the divine.
The ancient Rishis considered and knew God (the core infinite cosmic energy source) as the source of all manifestation, including our health, happiness, serenity, prosperity, progeny, victory, and fulfillment. They gained God’s grace by performing rituals to protect themselves from evil, harm, retribution, sickness, pestilence, and natural calamities.
Today, many of us are not in a state where we can control energy the way we want. Events that happen with us, our moods, and our joy are dependent on various external factors. Anticipating such a situation where humanity would also need such assistance even though their life isn’t yogic, many rishis dedicated their lives to create and document specific procedures that one can perform to gain specific benefits. Using this, a person trained in the vedic mantras can summon the correct energies and use it for the betterment of their family, society etc. can therefore fulfill dharmic, ethical wishes such as a house, money for family, children, prosperity etc.
As these procedures could be followed by anyone with the proper training and devotion towards God without necessarily needing to know how they work, they became popular and adopted among the Sanatana dharma households as part of their life. Once a person rises as a spiritual seeker himself and practices the right niyamas, japas, tapas, yoga, meditation etc, slowly the need for external help such as puja reduces.
So yes, God is everywhere and within each of us. Still, until that statement becomes a living reality, these pujas help us pass through different life stages and start increasing our connection with the divine and make our path towards spiritual progress more possible.
Hope this article helped you understand the purpose of puja and why puja is important. Even today, many of the households have this habit of conducting puja on a daily basis at their home mandir. Such repeated actions with clear thought processes are powerful transformative tools !