Chazal recount a story which illustrates this idea beautifully. The great Tana, Rabbi Chaninah ben Dosah, once saw his villagers pledging and donating sacrifices to the Beis Hamikdash. Witnessing this, he said "everyone is bringing up offerings to Yerushalayim and I bring nothing?" he wished to bring something but did not have the means.
He went to the outskirts of the city and located a certain stone. He then chiselled it and smoothed its surface until it was fit to be used for the maintenance of the Beis Hamikdash. He wanted to take it up to Yerushalayim and donate it to the Beis Hamikdash. Due to its heavy weight, though, he was unable to transport it himself, so he requested local porters to carry it for him. When they demanded five sela'im as payment Rabbi Chanina ben Dosah agreed but he did not have the funds. The men were not ready to carry the stone without the payment upfront and Rabbi Chaninah was now faced with this dilemma again.
Seeing his distress, Hashem sent five angels disguised as people. When he saw them, he asked them if they would take it for him. They agreed to do it also demanding the sum of five sela'im, but agreed for him to pay later on. However, they stipulated that he must assist them. He readily complied and gave his hand to help, when he suddenly found himself in Yerushalayim.
He looked around, wanting to pay the people who so graciously assisted him, but they were nowhere to be found. Seeking a solution on how to pay his debt, he went into the לִשְׁכַּת הַגָּזִית - the chamber of the Sanhedrin, the great court of Chachomim, located by the Beis Hamikdash. Hearing his story, they told him, "it appears that angels of Hashem carried up your stone to Yerushalayim", and absolved him from any payment.
(מדרש קהלת רבה א א)
This story reinforces the notion that if one is sincere in his desire to draw close to Hakadosh Baruch Hu, he will merit special assistance from Above to reach his goal, provided that the person himself does his bit and starts the process himself. Rabbi Chanina only had to stretch out his hand to help carry the stone and Hashem completed the task for him.