What is the evidence for the claim that performing good and kind deeds is a form of Da'wah (proselytization) in Islam?

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger. 

There is no doubt that good treatment and kindness to people are among the most important means for endearing Islam to them and encouraging them to embrace it. Allah, The Exalted, says (what means): {And who is better in speech than one who invites to Allah and does righteousness and says: Indeed, I am of the Muslims.} [Quran 41:33]

Ibn Katheer commented on the verse, saying, “Al-Hasan Al-Basri recited this verse and then said, ‘This is the beloved of Allah, this is the close friend of Allah, this is the chosen one of Allah, this is the most beloved of all the people of the earth to Allah. He responded to the call of Allah and called mankind to that to which he had responded, and he did righteous deeds in his response.’” [Tafseer Ibn Katheer]

What indicates the significant effect of kindness is that the Prophet, sallallahu ‘alayhi wa sallam, spent much of his wealth on winning the hearts of the disbelievers and encouraging them to embrace Islam, and it influenced some of them as intended. Anas, may Allah be pleased with him, said, “Never was the Messenger of Allah, sallallahu ‘alayhi wa sallam, asked for something but that he would give it. A man came to him, and he gave him a large flock of sheep and goats that filled an area between two mountains. So he went back to his people and said, ‘O my people, embrace Islam, for Muhammad gives so much charity as if he has no fear of want.’” [Muslim]

Dr. ‘Abd Al-Kareem Zaydaan wrote:

“One of the very important means of Da‘wah and encouraging people to embrace Islam is having a good reputation, praised conduct, refined manners, and moral values qualifying the person to be a role model and good example for others. Thus, he becomes a living manifestation of the teachings of Islam; people would see the Islamic concepts firsthand in him and, accordingly, become more attracted to them... An early precedent indicating that the good reputation of the caller to Allah plays a vital role in the Da‘wah and adds to his credibility, making it most likely that people would listen to him, was the incident in which the Prophet, sallallahu ‘alayhi wa sallam, informed his wife Khadeejah, may Allah be pleased with her, of what had happened to him in the cave of Hiraa'. She reassured him saying, ‘Rejoice, for by Allah, He will never disgrace you as you keep good relations with your Kith and kin, speak the truth, help the poor and the destitute, serve your guest generously and assist the deserving, calamity-afflicted ones.’ She listed his refined manners and good qualities out of her faith in him and to support him in spreading the truth.”

Dr. Ahmad Ghalwash, in his speech at the International Conference for Daʿwah that was held at the Islamic University in Madeenah, said:

“The caller to Allah is a brother to those whom he is calling to Allah. He is above them through advice and guidance. His need for their appreciation of him and confidence in him are obvious, and he cannot attain any of that except through refined manners generated by his respect of people and appreciation of them and his honesty and generosity with them as well as ultimate integrity in all his dealings with them. The Prophet, sallallahu ‘alayhi wa sallam, said, ‘You cannot encompass people through your wealth, so encompass them through your good manners.’”

Allah knows best.