I live in a built up suburb, have a tiny rear garden (and front garden) and have only been feeding the birds for a few months.
I have a few hanging feeders (one nyger seed, three large mixed seed, crushed peanut holder, one raised and one ground table, and two birdbaths (one high and one low). The large hangers have those tray attachments to catch falling seed and I put table food in those as well as on the table feeders.
That, given the area I have, is about the fairest amount of feeders I can provide and the birds descended within two days to feast. Granted the first comers were starlings but their example drew the sparrows and then came the blue and great tits, greenfinches and ... oh, I forgot the magpies and crows that were around anyway!
Foodwise I get the Ann Kennedy mix, the Aristocratic Superior High Energy one, to which I add sultanas and raisins, Atora suet granules, pinhead oats and rolled oats ... plus whatever else I have to spare ... rice or pasta etc. And I put out shell nuts for the jays, magpies and squirrels so that they can hoard them for the desperately cold days.
I think water makes the difference too, so if you have not put out bathing and drinking facilities for the birds that will swing the difference.
I do have cats, two indoors and four strays (for whom I provide feeding and sheltering areas, plus a hedgehog currently hibernating in a little house near the feeders, and two squirrles who call. I have not seen any birds taken by cats, and the birds and squirrels feed next to each other (I make sure the squirrels have plenty of food to their own taste and they have not yet disturbed the bird feeders in some nine months).
I had not thought, given that my rear garden is so small, and mostly tarmac for parking cars (which get left in the street so the birds do not get disturbed by cats who may hide underneath the cars) with paved surrounds, that I could decently offer the birds a feeding sanctuary. However, last summer I counted up to 40 sparrows and the same of starlings, four magpies, two jays, two carrion crows, a coal tit, great tit, blue tit, four greenfinches, two blackbirds and two goldfinches as every-day visitors. It is less frequented in the cold and I am concerned about the sparrows but the birds still come.
I do not have any trees. There is countryside not too far off, with trees and hedgerows and still the birds found me! My garden has 6 foot wooden slat fences on which they perch, which is nicely overgrown with ivy and up which I am training blackberry and raspberry bushes, firethorn and climbing roses. However, the birds know that I emerge each dawn, midday and mid-afternoon with fresh food and change the water and refill hangers and tables and they sit atop the roofs of the houses in the terrace and call out to one another when I appear. They cannot roost in my garden but they are safe to feed in it.
Okay, this was a long way of saying that even if you live in a build up area with a tiny, not grassy garden, the birds still find you and will come!