Should the amount of our giving reflect our trust in God to provide for our needs?

Short answer: Yes and No.
Long answer: Let’s see what the Bible says…

We should give out of our poverty.

Mark 12:41-44
41 Jesus sat down opposite the place where the offerings were put and watched the crowd putting their money into the temple treasury. Many rich people threw in large amounts. 42 But a poor widow came and put in two very small copper coins,worth only a fraction of a penny. 43 Calling his disciples to him, Jesus said, “I tell you the truth, this poor widow has put more into the treasury than all the others. 44 They all gave out of their wealth; but she, out of her poverty, put in everything—all she had to live on.”

2 Corinthians 8:1-3
1 And now, brothers, we want you to know about the grace that God has given the Macedonian churches. 2 Out of the most severe trial, their overflowing joy and their extreme poverty welled up in rich generosity. 3 For I testify that they gave as much as they were able, and even beyond their ability.

We should give out of our increase.

2 Corinthians 8:14
At the present time your plenty will supply what they need, so that in turn their plenty will supply what you need.

2 Corinthians 9:10-11
10 Now he who supplies seed to the sower and bread for food will also supply and increase your store of seed and will enlarge the harvest of your righteousness. 11 You will be made rich in every way so that you can be generous on every occasion, and through us your generosity will result in thanksgiving to God.

We should give when there are special needs.

1 Corinthians 16:1-3
1 Now about the collection for God’s people: Do what I told the Galatian churches to do. 2 On the first day of every week, each one of you should set aside a sum of money in keeping with his income, saving it up, so that when I come no collections will have to be made. 3 Then, when I arrive, I will give letters of introduction to the men you approve and send them with your gift to Jerusalem.

We should give to the regular support of believers in need.

Acts 4:32-35
32 All the believers were one in heart and mind. No one claimed that any of his possessions was his own, but they shared everything they had. 33 With great power the apostles continued to testify to the resurrection of the Lord Jesus, and much grace was upon them all. 34 There were no needy persons among them. For from time to time those who owned lands or houses sold them, brought the money from the sales 35 and put it at the apostles’ feet, and it was distributed to anyone as he had need.

We should be wise with the money God gives us, making sure it’s being used in ways that have eternal value.

Matthew 25:14-30
14 “Again, it will be like a man going on a journey, who called his servants and entrusted his property to them. 15 To one he gave five talents of money, to another two talents, and to another one talent, each according to his ability. Then he went on his journey. 16 The man who had received the five talents went at once and put his money to work and gained five more. 17 So also, the one with the two talents gained two more. 18 But the man who had received the one talent went off, dug a hole in the ground and hid his master’s money. 19 “After a long time the master of those servants returned and settled accounts with them. 20 The man who had received the five talents brought the other five. ‘Master,’ he said, ‘you entrusted me with five talents. See, I have gained five more.’

21 “His master replied, ‘Well done, good and faithful servant! You have been faithful with a few things; I will put you in charge of many things. Come and share your master’s happiness!’

22 “The man with the two talents also came. ‘Master,’ he said, ‘you entrusted me with two talents; see, I have gained two more.’

23 “His master replied, ‘Well done, good and faithful servant! You have been faithful with a few things; I will put you in charge of many things. Come and share your master’s happiness!’

24 “Then the man who had received the one talent came. ‘Master,’ he said, ‘I knew that you are a hard man, harvesting where you have not sown and gathering where you have not scattered seed. 25 So I was afraid and went out and hid your talent in the ground. See, here is what belongs to you.’

26 “His master replied, ‘You wicked, lazy servant! So you knew that I harvest where I have not sown and gather where I have not scattered seed? 27 Well then, you should have put my money on deposit with the bankers, so that when I returned I would have received it back with interest.

28 ” ‘Take the talent from him and give it to the one who has the ten talents. 29 For everyone who has will be given more, and he will have an abundance. Whoever does not have, even what he has will be taken from him. 30 And throw that worthless servant outside, into the darkness, where there will be weeping and gnashing of teeth.’

We should temporarily withhold our giving if it means taking care of our immediate family.

1 Timothy 5:8
If anyone does not provide for his relatives, and especially for his immediate family, he has denied the faith and is worse than an unbeliever.

We should temporarily withhold our giving if it means we won’t be going into debt.

Psalm 37:21
The wicked borrow and do not repay, but the righteous give generously.

Matthew 5:42
Give to the one who asks you, and do not turn away from the one who wants to borrow from you.

Romans 13:6-8
This is also why you pay taxes, for the authorities are God’s servants, who give their full time to governing. 7 Give everyone what you owe him: If you owe taxes, pay taxes; if revenue, then revenue; if respect, then respect; if honor, then honor. 8 Let no debt remain outstanding, except the continuing debt to love one another, for he who loves his fellowman has fulfilled the law.

Overall, we should give out of a willing heart.

2 Corinthians 8:12
For if the willingness is there, the gift is acceptable according to what one has, not according to what he does not have.

2 Corinthians 9:7
Each man should give what he has decided in his heart to give, not reluctantly or under compulsion, for God loves a cheerful giver.