Jagadguru Madhvacharya and Shripaada Jayateertha have provided one such explanation on this topic, which is one of the strongest and the best. This appears in Tattva Sankhyaanam and its commentary by Shri Jayateertha.
The first part of the argument is as follows: (1) anything composite is a dependent entity. It’s made of parts and as a result, depends on them. A wall depends on bricks for its existence. Everything is made of atoms and depends on them, as they are the individual parts of an object. Similarly, on a large scale, the whole universe too depends on individual parts that constitute its objects.
Shripaada Jayateertha, in his commentary on Tattva Sankhyaana, mentions the inevitable requirement of an independent entity, discrete from the set of dependent ones. Everything known or seen is dependent and therefore, they must ultimately depend upon something
(2) The entire universe too is a dependent entity, as shown in the first part of the explanation. It too is made up of individual components. So, it must be asked: on what do all of these ultimately depend upon?
(3) Now it cannot be supposed that this chain of dependencies is infinite. If we say A depends on B, B depends on C, C depends on D…., it is not even possible for A to come into existence in the first place! In other words, if the chain of dependencies were infinite, it would never have an end and so, A wouldn’t even come into existence.
Therefore, there should be an independent Tattva, on whom all the dependent Tattvas depend. This is the straightforward definition of ‘God’ or ‘Param Brahman’ as per the Hindu philosophy. The highest entity that all the entities of the universe depend on, is defined as God or Brahman. For this reason, the Brahma Sutras define Brahman as follows:
The cause of the origin and the rest (of this material creation) is Brahman.
-Brahma Sutras, Adhyaaya 1, Paada 1, Sutra 2
Now, Brahman cannot be a dependent or created entity, since that would again bring the issue of infinite dependencies, leading to conclude that none of the objects in the universe are caused. Therefore, there must be an entity, independent of all the causes entities, on whom everything depends. This entity is identified as God or Paramaatma, as per Vedaanta.
स्वतन्त्रमस्वतन्त्रं च द्विविधं तत्त्वमिष्यते ।
“The independent and the dependent — these two Tattvas (truths) are accepted to exist, by the proof guided.”
-Shripaada Madhvacharya, in Tattva Sankhyaana
Further, Shripaada Madhvacharya mentioned the following in the Dvaadasha Stotras:
यदि नाम परो न भवेत्स हरिः कथमस्य वशे जगदेतदभूत् ।
यदि नाम न तस्य वशे सकलं कथमेव तु नित्यसुखं न भवेत् ॥
"If Sri Hari is not the Supreme One, how did this world continue in His control? If the world is not in His control, why hasn't everyone attained eternal bliss?"
-The third Dvaadasha Stotra, Vaakya 5
The argument here is that an independent entity wouldn’t choose to be in misery. If we are independent entities, then how are we in misery? If we aren’t in the control of Bhagavaan, how are we still in misery and unable to achieve bliss? Therefore, from the aforementioned arguments, it follows that there is a Supreme Being upon whom everything depends, while He depends on none. Thus, Shripaada Madhvacharya declared in Tattva Sankhyaana:
स्वतन्त्रो भगवान्विष्णुः ।
The independent is Bhagavaan Vishnu.
सर्वभूतस्थमेकं नारायणं कारणपुरुषमकारणं परं
ब्रह्मोम् ।
Naaraayana, who pervades all entities, who is One, who is the casue of all causes and who is causeless, is Para Brahman.
मत्त: परतरं नान्यत्किञ्चिदस्ति धनञ्जय ।
मयि सर्वमिदं प्रोतं सूत्रे मणिगणा इव ॥ 7 ॥
(Shri Krshna said): “There is nothing higher than Me, O Arjuna. Everything rests in Me, as beads strung on a thread.”
-Bhagavat Geeta, Adhyaaya 7, Shloka 7
Thus, is the establishment of proof.